To give you an example: I had a very old system that I stopped using it for last 5 years until last month i decided to rebuilt that machine and make it operational. Specs:
Core 2 Quad Q6600 (released 2007)
Nvidia GTX 260 (released 2008)
I just added ssd and it works amazingly fine. I played tomb raider and in medium settings (1080p) i was getting 40-50 fps avg which was amazing for a 6-7 years old gpu. It plays cs-go, dota2, L4D2, AC2,3,4 on either medium or high settings easily.
A GTX 780ti will probably start aging after another 5+ years easily or 10 years if you SLI i assume x2.
Hope that helps you figure out how long it'll last