I will have a 5 hour, morning layover (7:30am -12:30pm) in Phoenix on the day after Thanksgiving. Is this sufficient time to leave the airport and see/do something in the immediate area? Any suggestions for nearby sites/activities and/or in the airport itself?

The Heard museum is a gem and you should be able to manage a visit during the layover.

I'd suggest the Botanical Garden. Very close to the airport, and the cactus and other desert growth is magnificent and unique. An easy taxi ride. The Heard Museum is also an idea, if you are into American Indian art and so forth.
http://www.dbg.org/

The Desert Botanical Garden and Heard Museum are two excellent options. Assuming my layover remains 5 hours long,I will probably visit the Botanical Garden, with the Museum as an alternative if the weather doesn't cooperate. Thanks for the suggestions!
What is the approximate travel time to the Botanical Garden from the airport?

less than 10 minutes from terminal 4, 15 minutes from terminal 2. including traffic.