I have iOS 8.4.1 on my iPhone 5s. Is it safe to update to iOS 10.2.1?

Hello,

We don't know exactly what the result will be. But on my iPhone 5S it worked perfect.

Before updating to any software please do a iTunes/iCloud backup.

How to back up your iPhone, iPad, and iPod touch - Apple Support

I don't believe anything will happen. In the case something does you will have a backup.

If you have a computer I will suggest making a encrypted iTunes backup. An encrypted backup save certain things a normal backup doesn't.

More info here:

About encrypted backups in iTunes - Apple Support

Others have made good suggestions but remember it is like your friends standing in a lake saying to you, "Sure, come in, the water's fine!" 👿

One thing nobody has asked is how old is your computer? iOS10 will require the newest iTunes which in turn will require a computer running OSX Mavericks 10.9.5 or newer which will exclude any Mac computer older than 7-8 years. If you are using an older computer then upgrading may adversely affect any really old software you have. Some people find upgrading has resulted in their having to buy a brand new computer and all the software upgrades and headaches that go with it.

With my old iPhone 5S I ran both iOS 9 and 10. The phone still works good. From my personal experience I would suggest updating.

The OP doesn't necessarily need a computer to update I'm assuming the OP will update over-the-air. I can see your point though. I wouldn't assume anything would happen with the update.

I would also want the OP to have iOS 10 as it has newer security features to protect their device and all the new features!

Hi

Go to settings iCloud backup now

Then update your software over your WiFi

Cheers

Brian