If I change the iTunes account info on my iPhone, will I lose everything on it?

Right so. I can't authorize the account on my new laptop as it is already authorized to 5 computers and I can't authorize any more than 5 (they're old hard drives I no longer have access to so I can't de-authorize any of them). I can make a new iTunes account on my new laptop, but the old iTunes account will still be on my iPhone.

What happens if I plug the iPhone (with the old account) into the laptop (with the new account - keep in mind the iTunes library on the new laptop is the same library that's on my phone as I had it saved to a memory stick. It's just the iTunes accounts that will be different). Will I lose everything on my phone?

You can deauthorize devices even if you no longer have them so there should be no need to create a new account if that is the reason. The iTunes library won't be deleted unless you choose to sync the phone with the new laptop. Even then it will warn you before you can proceed. If it's non purchased music and you have a backup you can always load it into the phone again since you have a backup.

But personally if you don't have to don't create a new account but rather deauthorize any devices you no longer own. It will be much easier when sync or backup.