Not too sure about this. I do know that gmail gives you a notice in the notification bar when you get a new email and lets you know which, if you have more than one account, it was on. However my school email I can't get to update like that
Having it check your email every 5 minutes probably isn't going to be great on your battery. Try it for a few days set to 5 minutes, and then a few days set at 10 minutes and see if you notice a difference in battery usage.
The best thing to do is have your email forwarded to a Gmail account (or have a Gmail account check your email) and then setup your phone to sync with that Gmail account. This way new messages will be pushed to your phone as soon as you get them with out having to constantly check. You can also setup Gmail to be able to send emails on the behalf of another domain, thus allowing you to do all your email tasks from a single account.
BTW - Google does have a great way for you to masquerade your gmail.com account as another account. As long as you can forward your other mail to your gmail.com account, and use SMTP to send as the other account, you can keep the same email address.