at&t iphone 5s and verizon iPhone 6

NO.

Verizon is a CDMA phone and AT&T is a GSM phone, so a Verizon CDMA phone will not work in the US on the AT&T network.

If you want to use your iPhone 6, then you will need to set up a contract with Verizon to be able to do so. Other than that and if you don't want to use it on Verizon then congratulations, you have just purchased a phone that you can't use. Either return it to your seller on E-Bay and get a full refund or sell it yourself again on E-Bay to someone who actually uses Verizon and can use the phone, but you can't unless you set up an account with Verizon.

Its my understanding Verizon iPhones are unlocked as a result of an agreement with the US government regarding spectrum. Here is an article that kind of sort of explains this...

http://www.cnet.com/news/confused-about-locked-vs-unlocked-phones-ask-maggie-exp lains/

From the article...

Verizon 4G LTE devices are unlocked out of the box

One thing to note here in terms of software phone locks is that all Verizon 4G LTE smartphones come unlocked out of the box. The reason why is that the spectrum Verizon is using to build its 4G LTE network had restrictions put on it by the Federal Communications Commission, which required the company to allow "open access" to the network. So as part of this provision, Verizon has decided not to lock those devices. That said, its 3G devices are locked.

This article details the various phone models and what networks and bands the devices work on. It maybe of some interest...

https://www.apple.com/iphone/LTE/