If I have an iPhone 5s, do I have to have it with me to pay via Apple Watch?

Good question.

Since it says that the watch has to be paired with the phone, I would assume that the phone must be within watch range for ApplePay to work. Best wait and see what the story is once the watches are released. Only 6 days to go.

Here is what CNet said about functions the Apple Watch can do while away from the iPhone (relative to your specific question) ...

Once you set up a credit card for Apple Pay to work on Apple Watch, it keeps working even when your iPhone is not attached. Double-click the flat side button, and you can tap to pay at any Apple Pay-ready store. It's easy to use and addictive. If the watch is taken off your wrist, you'll need to enter a passcode to use it again. Because Apple Pay doesn't use your actual credit card number, you can cancel it from your iPhone and deactivate your Apple Watch's Apple Pay function, even if the watch isn't online at all.