Lots of things to take into account for competitive gaming in terms of response. Refresh rate, response time, connection speed.
Ultimately it's all about what you're used to, and what feels foreign(in both directions). I know great players on a game called blacklight: retribution that play with 10ms Dell OEM monitors and 500ms connections. They play their lag lol.
Regardless, I used to use a 5ms monitor years ago. Never had an issue with shooters. I've always had a good connection though, stable. Regardless, I use a 60Hz 1ms 1440p monitor now and honestly notice very little to no difference from my old 5ms monitor. Just the random moment when I'm like, "Wow, I responded a lot quicker to that moment that x, y & z player.