The card is 9" which isn't that long. I'd say itd fit but it would help to have a picture of the inside. Also double check with a ruler, from the slot brackets to the first obstruction if it will fit.
PSU might be a problem, bottlenecking won't be though.
750ti shouldn't use more than 125w total (75w from PCIE + 75w from 6 pin) i5 4440 is 84w.
At any rate, make sure you measure.
Edit: Editted, didn't know the FTW edition had an additional 6 pin.
@OP just get a normal 750ti, don't worry about the FTW edition.