Yes, you can use Snapchat with your iPod Touch 5. According to the official system requirements posted on the Apple Store, you have the possibility to install this app on iPhone, iPad, and iPod touch with iOS 7 or higher. If your iPod has iOS 7 or higher, hen you can install it. Use the App Page or the Store application in your iPod to install it.
App page: Compatible with iPhone, iPad, and iPod touch: https://itunes.apple.com/en/app/snapchat/id447188370?mt=8