Do I need to upgrade ethernet if upgrading router?

So finally getting around to upgrading my roughly 10 year old router to this mesh setup:

https://www.newegg.com/tp-link-deco-xe75-pro-mesh-wifi-system/p/N82E16833704668?Item=N82E16833704668&_gl=1*rk4wl4*_gcl_au*MTg5MzM5MTgxMS4xNzcyNTY2NzMzLjc0NTcyOTg3OS4xNzcyNTc3OTI0LjE3NzI1NzgwMDg.*_ga*MTQwNTM3MzgyOC4xNzcyNTY2NzM1*_ga_TR46GG8HLR*czE3NzI2NDIwNjgkbzMkZzEkdDE3NzI2NDIwNzAkajU4JGwwJGgyNzIxNDg3MzI.

I know my current ethernet cables are cat5. We don't have fiber in our area and my plan has 1.2gbps speed. Given my current plan speed, do I need to swap my cables out for cat6? Also, thoughts on the mesh setup before I pull the trigger? The 2nd unit will be hardwired and placed in my bedroom ( I believe that's called wired backhaul?)