Is iOS 10.3 good for iPhone 5s?

Also, since you mentioned you haven't updated to any iOS 10 versions here is some information on the iOS 10 - 10.3 updates. Download iOS 10.0 - iOS 10.3 Information

In case you need it, here is an article that will help you update your phone.

Update the iOS software on your iPhone, iPad, or iPod touch - Apple Support

In my opinion though, as you can see these updates add some very important fixes, so the short answer to your question is: yes, update.

iOS 10.3 update is "available for iPhone 5 and later." You should always keep your phone updated, this is very important. Updates include security improvements, bug fixes, as well as new features, etc. More importantly than new features though, not updating could impair the proper functioning of your phone and expose you to security risks.

For example, here you can read about the security content of iOS 10.3 About the security content of iOS 10.3 - Apple Support

My wife and I use same iPhone as yours, and both has been updated to 10.3 version. The iOS runs smooth and fluid like it was built only for iPhone 5s. It can buy you more storage room due to Apple new filing format. I feel my battery life increases a little bit with this iOS.

But according to my wife, there is a little problem she has. She can't open password protected PDF attachment on her email.

As for me, I can't read reader comments from several news sites that I visited.

I don't know if both problem have something to do with iOS 10.3

My wife already sent a feedback to Apple. I hope there will be fixes in the future to improve user experience.

I Just updated my iPhone 5s 16gb and got back about 1gb of memory! So all looking good so far

Yes, the same problem opening password-protected PDF files after iOS update.

Am using iPhone 5s and it support 11.0.2 and working well

But new 11.0.3 downloaded but it has been crashing networks issue