Hello!
I can absolutely understand wanting to save this progress! Most games now have some sort of sign-in ability that allows you transfer progress between devices (IE through Facebook or a service of their own). You would then sign into the game on the new device and the data would transfer over. A word of caution, do not wipe your Galaxy 5A until you are absolutely certain that the 7A has all the data you wanted to transfer.
If you let me know the specific game I can dig into this further for you and see if there is a step-by-step guide available!