If I buy a used Iphone 5, will it be Pay as you go?

I'm going to buy a used iphone 5 on ebay, but when I get it, will I have to pay monthly? Or is it pay as you go? Also if the iphone is on vodaphone, when I get it can I change it to my present service provider EE?

The SIM is the thing that defines if a phone is contract or PAYG so all phones can be either.

Yes the phone can be "unlocked" to be used on any network.

Be very careful if buying off Ebay as many are locked/stolen phones and one you pay you will get nothing back if it is permanently blocked.

It is likely that the phone will be PAYG, as it is being sold on eBay. However, I would try and ask the seller just to make sure.
You will definitely be able to use the phone on EE if the phone is unlocked (another thing to ask the seller!). If it isn't already unlocked, you will need to get it unlocked from the current network before you can use an EE sim. Unlocking costs around £10, and will allow you to put ANY sim into the phone.

It depends on how you set it up after the fact. Its more about the SIM in the phone than the phone itself as far as pre or post paid is concerned.

You'd have to inquire about unlocking services or try to find one that is already unlocked to use.