I plan to go on a 5 day trip to Leh, Ladakh, and am looking for recommendations for luxury hotels.
It sounds great that you are visiting Leh. I can suggest you "The Grand Dragon Ladakh" http://www.thegranddragonladakh.com/ as one of the luxury hotel in LEH.
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I will recommend Nimmu House Ladakh. It is a 105 years old Royal house which is now converted into Luxurious Boutique Hotel in Nimmo.
Do check http://ladakh.nimmu-house.com/ you can contact Mr Amul +91 99905 83183 for further information.
The Grand Dragon Ladakh is definitely the one you should check..
Gomang-Boutique Hotel or Ladakh Sarai are the best