Swapping out the headphones was a good idea.
Are you sure that the files you're playing were converted
to the right file format for IPOD? Files can play through ITunes , yet still may not be compatible with your 5th Gen.Ipod.
IPOD plays back MP3, WAV, AAC, AIFF, Apple Lossless and Audible 2,3 and 4 audio files. Make sure the Audio/ Video files are good?
Upload a good file from your music CD and then play back on IPOD. This will give you another solid check
that your files are not causing the problem vs. your IPOD.
Lastly--
You may want to take it back for an exchange if trouble-shooting becomes to much for you.