Well Id have to say that I dont know if its possible to pick 5 songs from any given decade. You run in to all the usual problems in picking such a small quota--are you picking songs that are most popular, or that you personally like the best, or that were most important in developing the genra, or that sold the most copies, or are you selecting one song from each genra etc...
I like all the songs they chose (in particular strange fruit) but I agree summertime should have been there, but so should any of a number of songs by the Carter Family  , Charlie Patton , Son House, Count Basie,  Ellington...
...Still, its always good for debate, lets just not get together to listen to our favorite 10 best albums of all time.
s