Q: unable to skip payment options while registering new Apple ID in to iPhone 5s

Hello there, Question. 

It sounds like you are trying to setup a new Apple ID on your iOS device without a credit card or payment method. The following Knowledge Base article offers great insight as to how and even provides a link to why you may not see that option:

Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Support

On an iPhone, iPad, or iPod touch

1. Open the App Store, iTunes Store, or iBooks Store.
2. Choose any free app, song, video, or book.
3. Tap Get next to the item, then tap again to get it.
   
4. When you're asked to sign in with an Apple ID, tap Create New Apple ID.
5. Follow the onscreen instructions. When you're asked for payment information, choose None. See what to do if None isn't showing or you can't select it.
   
6. After you enter all of the information required, you'll be asked to verify your Apple ID by email. You must verify your Apple ID before you can begin using it. Didn't receive the email?

If you use Family Sharing, and you’re the family organizer, you can’t set your payment information to None. You'll need to use a credit card or debit card.

Thanks for being a part of Apple Support Communities.

Kind Regards.