I've been suffering with the usual iffy Infinity speed and connected devices dropout problems that a number of other posters seem to suffer.
I thought I'd post elements from a (2 hour!) discussion I've just had with BT Support as it may help you highlight what's causing your problems and/or may help you decide whether BT broadband is for you. I've had repeated discussions with BT about the problems and, along with others, began to suspect that the root cause is the HH5.
I've now had it confirmed by BT support staff that the HH5 cannot cope with what, in my opinion, is a normal number of device connections, whether wired or wireless. The key quote from BT support is 'the home hubs are not meant to be connected to more than 4-5 devices, I am afraid'. So, if you've a couple of smartphones, a Sky box and a laptop connected, you're maxxing it out, so expect unreliability.
I've asked for an alternative to be supplied (such as a Draytek), but my hopes aren't high. This problem's now being escalated to Tier 2, but I doubt they'll be able to do anything magic with the HH5. I'll have to seriously consider leaving BT, as the reliability of the HH5 just isn't good enough.
Hope this helps others.
If you find that the Home Hub does not meet your needs, then you are free to purchase your own alternate router.
For what it is worth I have in excess of 10 devices connected wired and wirelessly (including 2 BTTV boxes) with the HH5 without issue.
In theory the only limit should be the number of IP addresses the hub can allocate, i.e 253 on one subnet.
That is absolute rubbish from BT support and just poor training.
The Homehubs are actually pretty decent hardware wise and can handle WAN to LAN throughputs that many other high end routers struggle with which is normally CPU dependent.
Shame about the firmware though but even on my HH3 I had upto 30 devices working without issue.