You play something on your bass, the signal reaches the system, it takes a certain amount of time (i.e. latency) to be produced by the monitor speakers and then additional time (i.e. more latency) to leave the speakers, travel through the air and reach your ears. If you're using headphones this is effectively not a consideration. If you're using monitors in the room then it absolutely is a consideration and most definitely is the way it works. As you move further from those monitor speakers the amount of latency increases since the signal from your bass reaches the interface at a higher speed than the sound travels from the speakers and to your ears. If you're ~3' away you've incurred ~3ms of effective latency. I don't often find myself that close to the monitors when playing through a digital or even an all-analog system. 6' (~6ms of latency) is pretty common when I'm both the bassist and the recording engineer. 10-15' (~10-15ms of latency) is pretty common when I'm in a larger studio than my own and tracking from the control room. These times are somewhat exacerbated when rear and sidewall reflections come into the picture that result in comb filtering, which typically affects the midrange frequencies on a bass and can result in a thinner and softer sound with less attack, thereby making things feel even less tight. Despite all that I'm sure you would still be able to play without your sense of groove being completely destroyed, as you put it.
I'm not trying to be condescending, although I'm probably failing at that, but I felt the need to chime in regarding your 5ms claim. If something is completely destroying your sense of groove it is certainly not 5ms of latency in the monitoring path ahead of the latency due to distance unless you're standing a huge distance away from the monitoring source.
