The PS4 Pro is designed for playing on a TV. And there, the average for input lag is around 40ms for most TVs. The response time of 5ms is excellent in comparison.
5 MS is fantastic. Even for PC gamers 5 MS is acceptable.
1 MS monitors are usually useless because TN panels have more input lag, I recommend watching Gamers Nexus on Youtube on this topic.
On the PS4Pro it doesn't matter at all, it has bottlenecks somewhere else. If you play on 4k the weak graphics card can't keep up with the 60hz refresh rate anyway. The PS4 is designed for TVs with extreme lags anyway, even if you have a 5ms screen, the real lag between controller input and monitor output will be much longer.
I still recommend buying a monitor and not a TV. The quality of monitors is far superior in every way.