Are big files bad for your iPhone?

I've got a spare 7Gb on my 32GB iPhone 5 and was wondering if downloading a large game onto it would make any difference to long/short term performance? I had previously had an old iPod which was jammed full with music and even after I took the files (most of) off it still performed slow, though it may have been for other reasons. Will is affect my iPhone?

Probably depending on how large the game is. If the system gets almost full it will affect the speed of the device noticeably

As Zack said, if yOur hard disk gets full, for example having few hundreds of megabytes free, it will get pretty slow. So don't go and download a 7 or 6.5 GB app, leave 1 or 2 GB free.