Is a 5070 Ti build enough for 4K gaming, or should I save for a 5080?

A 5070 Ti is a solid 4K choice if you're okay with upscaling and adjusting settings. It won't run every demanding game at maximum settings with path tracing at high frame rates, though. Check benchmarks for the specific games you want to play, especially with path tracing enabled.

For an extra $400 to $500, I'd have a hard time justifying the 5080 on a tight budget. It is faster, but whether that extra speed matters enough depends on the games and settings you're aiming for.

For shooters, pay attention to the actual frame rate before frame generation, not just the displayed number. Generated frames can make motion look smoother, but they don't give you the same responsiveness as rendering more frames normally. Upscaling or lowering settings may be a better first step when responsiveness matters.

Don't overspend on the CPU just because the screen is 4K. At that resolution, demanding games often run into the GPU's limits first. The CPU still matters for high frame rates, though, and using upscaling can shift more of the workload toward it.

Without the full parts list, nobody can really check the build. Post the CPU, motherboard, cooler, memory, power supply and case, along with your budget and local prices.

Also compare the 9070 XT if it's noticeably cheaper where you are. Performance varies by game, and it can be competitive without ray tracing. For your interest in path tracing, though, compare benchmarks with that feature on before choosing it over the 5070 Ti.