Reaching internet from a BGP router

Hi!

Diagram I'm setting up eBGP between the ISP and my client's network. That is not a big deal, public services work wonders.

Navigation traverses through this router - which is an F5 - and goes to the internet NATted to a couple of IPs on the public range.

Now, absolutely everything that should reach the internet does, except for the F5 itself. Since it does not go through the F5, its packets are not NATted, and thus, come out with its real IP (the peering network). This network, of course, is not published to the internet, so the F5 does a couple of hops and then dies.

How do I make my device reach the internet?

Thanks!