I am on Windows XP and I want to connect my iPhones 5s (iOS 9.3) to my iTunes

You're in a bit of a problem. For iOS 9.3, you need a very recent version of iTunes. And in turn, that needs a recent version of the OS. In this case, the bare minimum in a PC is Windows 7. No way around this.

I was in a similar pickle last year. My Mac had a OS X version that could not handle iTunes 12.3, which was needed for iOS 9.2. I ended having to upgrade to the latest OS X version, then the latest iTunes and now things are cool again.

You're in a bit of a problem. For iOS 9.3, you need a very recent version of iTunes. And in turn, that needs a recent version of the OS. In this case, the bare minimum in a PC is Windows 7. No way around this.

I was in a similar pickle last year. My Mac had a OS X version that could not handle iTunes 12.3, which was needed for iOS 9.2. I ended having to upgrade to the latest OS X version, then the latest iTunes and now things are cool again.

There is no provision for downgrading your iOS version - however there might be a ray of hope for you, at least in the short term. You were not very specific about your current iTunes version, but I suspect it must be 12.1.2 (check Help > About iTunes). The last version to support XP, and the only version with support for iOS 9 that can be installed on XP is Download iTunes 12.1.3 for Windows (32 bit).

That version might solve your problem for now, but you must be aware that XP is a dinosaur that needs to be replaced. The last seven versions of iTunes cannot be installed on XP, Google Chrome just ended support for XP, etc. The new iPhone SE cannot be supported with iTunes 12.1.3, which means it cannot be supported with XP. In about five months, iOS 10 should be released. If you are still relying on XP, then you will have to avoid that upgrade like the plague.

Yes