If Touch 7 is out of your budget, would there be not too much difference between 5 and 6?
Get atleast the 6th gen. The 5th gen is horrendous now. Extremely slow on iOS 9.3.5 (that's the highest it can go, and most apps don't work anymore on iOS 9, they require atleast iOS 10 or 11 by now), it only has the dual-core A5 chip from 2011 which is extremely slow by today's standards, only 512 MB RAM, 5 MP Camera only, and no 128 GB option.
Trust me, iOS 9 with the A5 is no fun. So many people complained, Apple should have never given iOS 9 to the A5 chipset devices. It's horribly slow, but iOS 10 on the iPhone 5 (A6 chip) or iOS 12 on the iPhone 6 / 6th gen iPod (A8) is fairly decent.
6th gen is a much better option. A8 chip with 1 GB RAM, it can support iOS 12.4.3, so all your apps work, 8 MP camera with Slo-Mo if that matters to you (anything under 8 MP is outdated if you ask me), and a 128 GB option, so perfect to store a lot of music. The 6th gen didn't had that many new features over the 5th gen, they just improved the overall device.