Chosen Solution
Hello I have an Ipod touch 5 generation where the bottom half of the screen has come loose and I cannot force it back in place
I have attached a picture of the Ipod and I hope it is clear enough to see the issue. -Thanks for your time!
Based on your answer to @jwongrocks suggestion, it is clear that your battery is defective and has started inflating the protective pouch. This is not only a defective battery but it is now becoming a fire hazard. You need to open up the iPod, remove the battery (without puncturing it) and dispose of it safely (check your city or local hardware store). Note, the battery does require some soldering skills. Once that is done, why not replace it with a good battery and revive your iPOd.
Try opening it up, maybe there is something in the Ipod that is not letting the display screen from closing.
The bottom half of the screen is held in with adhesive, if there is any dust or grime on this adhesive the screen will not rebond to the rest of the device. If this is the case, you need to fully lift up the display assembly and replace the adhesive with something akin to double sided foam tape. iPod Touch 5th Generation Display Assembly Replacement Best of luck.