Is it safe to upgrade iPhone 5C to iOS 9?
The iPhone 5C will run iOS 9 fine, as iOS 9 requires no greater hardware than iOS 8. My inferior iPod Touch 5th gen (comparable to an iPhone 4S, two years older than the 5C) became slow upon upgrading to iOS 8 but didn't get any slower when upgrading to iOS 9.

As always, do a backup before upgrading.