Should I update my iPhone 13 to iOS 17.5.1?

Was your device Jailbroken? If that's the situation, please be informed that attributing the issues to iOS updates may not be accurate.

I have been updating my devices ever since I bought my first device in 2009. iPhone 3Gs, 4S, 5, 6, SE (1st Gen), 7, 8 and iPhone 12 Pro, iPad Pro, iPhone 13, Macbook Air 2019, MacBook Pro 16"

I never had any issues with any iOS, iPadOS, or macOS updates to date.

I would personally recommend everyone update their devices instead of listening to rumors from people who may not have kept their devices free from any spurious software.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware if it is updated to the latest iOS/iPadOS unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed them on your device or/and have Jailbroken. 

iOS updates generally aim to enhance user experience, boost security, and fix bugs rather than disrupt core features. Issues after updates might stem from underlying, unmentioned factors. Updates won't typically alter personal data but may refine settings or features. Backup before major updates for safety. Review Apple's update details and backup advice for a smooth process.

This seems purely coincidental so please check the Setting on your device.

See what each update does: About iOS 17 Updates, About iOS 16 Updates, About iOS 15 Updates, About iOS 14 Updates, About iOS 13 Updates, About iOS 12 Updates, and so on...

I should update my Iphone 13 to 17.5.1?

Yes, if you want your phone to have the most up to date security settings.

No, if you don't.