Try this.
sudo add-apt-repository ppa:ubuntu-toolchain-r/test
sudo apt-get update
sudo apt-get install gcc-5 g++-5
apt-get autoremove
This should work in Linux Mint if I'm not mistaken, as its still using the same respository.
sudo apt-get respository ppa:ubntu-toolchain-r/test
This will install you the correct respositories you need for the computer. Some packages are not automatically known to the computer so you need to install the respositories so the computer can install it.
sudo apt-get update
This will update your computer and all packages and the respoitory, this wil ensure it will now work
sudo apt-get install gcc-5 g++-5
This will install the gcc-5 version you wanted.
sudo apt-get autoremove
When you install certain stuff, some things are no longer needed. Maybe a required package from a previous version that you no longer need, do this to conserve space.