Stop downloading emails

The problem is located on gmail side.
Go to Settings/Forwarding and POP (in your gmail account)
Choose POP Download : Enable POP only for mail that arrives from now on.
That should solve it.

5,000 messages ?
first of all you have too many and probably old emails. Another option is to create a new folder ( name it whatever you want - old emails ) select the old emails that you think you can move over, copy and paste to your new created folder. But make sure that all your old messages are in the new folder and only then you can delete your old email.

I wanted you to know that the default gmail setting is for recent setting which only downloads the last thirty days worth of e-mail

I'm having the same issue. I use Apple Mail on my MacBook and it works fine (i.e. doesn't download everything I have archived).

I have Gmails POP enabled for mail that arrives from now on, i deleted the account from my iPhone that got on there w/ the first sync and set it up again and I still get all the messages that are archived. The messages are archived automatically when a computer uses POP to access them from Gmail.

I also do not have forwarding on, nor do I bcc myself. It works fine on my Apple Mail, but not on the iPhone.

I might also add that my POP email through my school is working great, though there are no emails archived on it.

So I guess my essential question is, how do I get my iPhone to not download all 110 messages that are archived in my Gmail account like my Mail on my MacBook does???