leopoldtrepper, you should install programs from repositories
and not from source code. From the beginning you should've executed
# apt-get update; apt-get install firefox
The same command anytime you wanna update your browser. But in order for any program to be updated from repos it first has to be compiled and uploaded to repos by maintainers of the distro. That doesn't always happen instantly, so whenever a new version of Firefox is officially out, it takes several days for this version to become available for Mint/Ubuntu. Also, as been said, run
# apt-get update; apt-get upgrade
to update all programs in your system.