How can I run a current browser on older MacBook?
All MacBook Pros produced mid/late 2007 and later (MacBookPro3,1...) can be upgraded to at least OS X 10.11. 

So install OS X 10.9 or later on your (mid/late 2007-...) MacBook Pro (3,1-...) and enjoy the latest Google Chrome and/or Firefox browser.

The system requirements for Firefox 49 are 10.9-10.11 and for Google Chrome 54 10.9 and later