Probably because the TF-39 used on the C-5 was the ancestor of the CF6-80C2. The engines are similar enough to not require major redesigns of other subsystems on the C-5. They are also similar to the engines used on Airforce One and the E-4B's.
I can't hide my bias towards P & W being a former employee. Your knowledge of GE engines makes me think you have some experience with them.
My then girlfriend (my wife of over 10 yrs now!) did C-17 Flight Test, great bird.