Whether it's 5ms or not will depend on location and the details of how the routing works. I've just pinged www.bbc.co.uk
from where I live (Maidenhead) and that gives a stable 8ms on BT Infinity 2.
One thing to notice is that ultimately geography wins out (just try pinging a known US or even Australian site). The typical refractive index of the core of monomodal fibre is about 1.62 meaning that light propagates through it at about 185,000 km per second. That sounds quite fast, but it means every 90km of fibre adds 1ms to ping times (as it's a there-and-back journey). Fibre also rarely runs in a nice straight line between source and destination, and every hop and switch adds its own bit of extra latency.
Generally what matters most is not the absolute value of the latency (within reason), but whether it is stable or not. Zen do have a good reputation for this, probably because they don't scrimp on network capacity.
nb. in the US, latency times on electronic trading is so critical that some providers of electronic trade exchanges have built data centres to host trader's servers with equal length LAN cabling in order to equalise latency at the data centre level. Conceivably gaming companies could also equalise WAN latency (by introducing artificial delays on shorter links). There have been proposals to do this as a basic network service.