The shortest time for this trip is 44 hours of driving which works out to about 9 hours a day. Breaking this down into 5 days that are approximately equal, I come out with Boston
Day 2 - to Des Moines
Day 3 - Fort Collins
Day 4 -Beaver (Utah)
(This is the shortest leg at 565 miles) I originally had you stopping in Salt Lake, but that makes the trip longer. Beaver is at the end of I-70 where you join to I-15 so it is a truck stop kind of place but there are motels there.
Day 5 -Los Angeles
via Las Vegas (511 miles)
If you want to go on past Beaver and stop in Las Vegas on Day 4 to make the last leg shorter, the distance on day 4 would be 800 miles and the last leg to LA would be under 300 miles.