While I am not from the Portland area, my brother currently lives there. Here are a few of his suggestions:

City sites include Washington Park, the International Rose Test Garden the Japanese Gardens, the Pearl District (the first Thursday of the month), the Alberta Arts District (the last Thursday of the month), as well as the Hawthorne and Mississippi districts.

There are breweries all over the place BridgePort BrewPub, Deschutes Brewery, Rogue Distillery and Public House, Burnside, and Amnesia Brewing.

Multnomah Falls and Columbia River Gorge are great areas for exploring the outdoors, and there is also the Portland coast (Astoria and Cannon Beach (where the Goonies was filmed)).

In addition, there is the Oregon Zoo, the Oregon Museum of Science & Industry (OMSI), and the Portland Art Museum.

Shows at the Arlene Schnitzer Concert Hall or the Crystal Ballroom are always a blast and apparently Shanghai Tunnel Underground Tours is a company that explores Portland's old tunnel system.

Portland also has some great eateries, with two well-known establishments being Voodoo Doughnuts and Salt & Straw Ice Cream.

Hope this helps!

Oh I'm so glad you have 5 days! You'll certainly be able to fill them. I'm going to refer you to some answers that I've given to other Portland questions and then give you the clifnotes version below that lists kayaking and hiking areas that are just stunning.

http://www.trippy.com/question/Portland-Outdoor-sports-in-and-around-Portland  

http://www.trippy.com/question/Portland-Nature-y-spots-in-Portland#answerItemView_52abebcfe4b0d3459639ae13

http://www.trippy.com/question/Portland-Spots-for-nature-lovers-around-Portland 

http://www.trippy.com/question/Portland-Places-to-see-in-Portland

The big must-see locations are the Columbia River Gorge National Scenic Area which you could do in a day or longer if you want to do one of the longer hikes and camp.

Do go and see the International Rose Test Garden. It's free and has amazing views of Mt. Hood.

That being said, if you have time, drive up to Timberline Lodge for a day. The lodge is beautiful and there are amazing hikes there as well.

The beach isn't horribly far. Seaside (Oregon) is too touristy. Tillamook has the best ice cream at the Tillamook Cheese Factory. Cannon Beach has the best tide pools when the tide is out.

If the weather is nice, just walk. Enjoy the typical Portland vibe. The "Keep Portland Wierd" sign is across from Voodoo Doughnuts near Burnside road. Powell's Books is one of those amazing places you can get lost in (and have a great cup of coffee). Between Powell's and the walk towards Pioneer Courthouse Square, you'll come across an entire city block full of food trucks. Just walk, stop for random bites and beer, and enjoy the wierdness that Portland embraces.

Most of the people have given you some cool attractions to see, but I will try to fill in the blanks on a few other areas.

You are coming at a great time of year for sure, the rain should be gone and outdoor day drinking should be in full swing. If you are here at the last full weekend in July, check out the Oregon Brew Fest, a massive beer festival that takes over the waterfront from Wednesday - Sunday.

If you have access to a car, head up for a "beach day" at Sauvie Island where there is good people watching and you can hang out and drink a couple beers. It makes for a comical day. Also, head out to Hood River and go to Pfriem Family Brewers and Double Mountain Brewery & Taproom.

Also, there have been a string of great brewery openings including Breakside Brewery, Ecliptic Brewing, StormBreaker Brewing. For great places to get beer I would highly recommend APEX, Bailey's Taproom, Green Dragon Bistro and Pub. If you want good, strong beer and one of the most famous places in Portland, check out Hair of the Dog Brewery & Tasting Room. If you want to spend a day in the sun, eat some great cart food, drink German beer and make a day out of it, head to Prost! in the Mississippi area.

For food that are staples of Portland:

Escape From New York Pizza

Le Pigeon (can be expensive, but share plates and you can get out reasonably prices ($60-80 total)

Nuestra Cocina for awesome mexican

Pok Pok Restaurant for Traditional Thai - very famous nationally

Tasty N Sons for Brunch or for amazing Swedish brunch check out Broder Cafe

Toro Bravo is great spanish-style food served as small plates

There are tons more, but hopefully that trims it down for you.

So many things!

For the outdoors-y stuff, check out the Columbia River Gorge National Scenic Area (one of the stops is the famous Multnomah Falls). There are a ton of trails along that way. If you don't want to rent a car, Forest Park is a good option in the city. Also the Japanese Gardens, International Rose Test Garden, Laurelhurst Park are in-city options.

As for beer, there are even more options! Cascade Brewing Barrel House has great sour beers. As does APEX, Gigantic Brewing Company, Imperial Bottle Shop & Taproom, and The BeerMongers. Hawthorne Hophouse is my personal go-to bar.

As far as the budget goes, you're in luck. The parks are all free! Portland is completely beautiful, and you'll love walking around.

For cheap food, also check out one of the many Food Cart pods. My personal favorite cart is Potato Champion. Most of the carts are great bargains.

Hope you enjoy your trip!

The Portland Saturday Market and Voodoo Doughnuts are a must! Multnomah Falls is a very convenient waterfall with some hiking trails, but can be crowded. So many breweries, I have only been to a few and can't say I'm a beer connoisseur, but I've enjoyed BridgePort BrewPub and Rogue Ales Public House in the Pearl District, and while in the area, you should stop in to Powell's City of Books. I can spend an entire day there! Burnside Brewing Co. lets you get a sampler of as many beers as you want for only $1 per, and they have good cheese curds. I feel like you can't go wrong with restaurants in Portland. Fuller's Coffee Shop has great breakfast at great prices with a diner eat-at-the-bar atmosphere. Bartini has great happy hour prices (all evening Sundays) with flavorful martinis, fondue, salad, and other tasty things. That's all I've got, I'd love to do more outdoorsy things there myself, and hope you have a great time!

If you have half a day, a car, love animals and don't mind taking a small road trip down the 5 freeway, there's Wildlife Safari in Winston.

You drive your car through the safari and check out all the animals (sometimes they block the road so you just have to wait).

They also have regular zoo exhibits to walk around and see and other paid activities like giraffe and elephant feeding. It's all fairly inexpensive unless you do some of the pricier encounters like the lion feeding.

I also went in July and the good thing is the sun was up until 9pm or so and I was back in Portland by 4pm or so to do other things. 

You're coming at a great time! The weekend you're here there's an incredible blues festival on the downtown waterfront - definitely worth going to, day or night: http://www.waterfrontbluesfest.com.  The Waterfront Park Trail is a great place to watch the fireworks, too, as is Fort Vancouver National Historic Site across the Columbia.

While downtown, you can walk, bike or segway (http://www.portlandbysegway.com) for miles along the waterfront, both sides, crossing the many bridges. Or you could hike around in Forest Park, the largest  park in city limits, or Mt. Tabor Park, the only (extinct) volcano within city limits.

There are lots of outdoor activities to enjoy here, and I'll let others chime in (especially cyclists and wind/kite surfers). My own passion is kayaking, and you can rent single/double kayaks and canoes many places to see the sights from water-level.

A favorite is Willamette Falls  (rent from NW Outfitters/NRG Kayaking in Oregon City), or you can go around Ross Island  with great city and natural views, including the houseboats of Oaks Bottom (rent from Portland Kayak Company  on Macadam). Nearer the Columbia River, you can float the Columbia Slough and drop into the Island Cafe on Hayden Island (rent from Alder Creek Kayak & Canoe ).  There are lots of water adventures in this region - these are just a few of my top picks….

Look here for beer recommendations: http://www.portlandmonthlymag.com/eat-and-drink/articles/best-beers-0710/2/

And here for dining recommendations: http://www.wweek.com/portland/cheapeats

ENJOY!

Edit: I forgot to mention our famous food carts, which are established at various blocks around town. Learn more here:http://www.foodcartsportland.com

These are great answers that cover most things - but you should also consider just biking around the city - the weather should be great - Forest Park, Eastbank Esplanade, Alberta Arts District and Mississippi Ave, Mt. Tabor Park, Belmont and Hawthorne Neighborhood

Visit the Columbia River Gorge National Scenic Area for waterfall hopping, and stop in Hood River to see one of the best summer wind-sport destinations of the world. On any typical day between June and August, there are literally hundreds of kitesurfers and windsurfers on the water.