Hi @jab7416 and welcome to the forum. As to your question, you likely can swap the 560ti with a 970 with some caveats.
First, you will need to make sure that your power supply can handle the extra load of the newer card, and that it has the power connectors needed. Newer cards like the 970 will require two PCIe power connectors. If the PSU that came with your PC was modular and you still have the cabling kit bundled with it then you may be OK on that score.
Secondly, given the age of your motherboard and CPU, the bandwidth simply won't be available to get full use of the card. Speaking from experience I had a 4th gen i5 in my PC with a GTX1080, and recently upgraded to a 7th gen i7 whilst keeping the GPU the same. The difference is phenomenal.Your CPU and motherboard will basically strangle the 970 so it won't run at it's full potential. And given some games are very CPU bound (like Battlegrounds and ARMA III) then upgrading the GPU alone will not give you the performance increase you would hope for when spending the kind of money you are looking at for a 970.
TL;DR It will work, but the rest of your PC will essentially starve the card.