I am exempted from a transit visa for the UK as I am flying from South Africa to the USA via the UK. I am arriving & departing from T5 on BA. I am not allowed access into any of the BA Lounges at T5 & will be in transit for 9h30m so looking for a lounge where I can pay for access to have a shower & rest. Am I allowed to commute between terminals & which lounges will I be allowed into without a transit visa for the UK. Are there immigration checks between terminals?
No, you are not allowed to get airside in the other terminals without a same day boarding pass departing from the terminal in question. Even if you do successfully get into the other terminals (actually it is possible to get access to Terminals 2,3 and 4 without a boarding pass but only if you really know your way around Heathrow), the lounge staff are required to deny you access, unless you are departing from the same terminal. Plus, you will also have trouble leaving the terminal again.
Aspire is opening an independent pay-for-access lounge in T5 underneath the south lounge complex, but I am not sure when it is to open.
If you are able to go landside via immigration, there is a Regus business lounge in the T5 building, with access available for payment. Regus also gives away free lounge passes on promotions, which can probably be found by Google.
To your other questions, there is no immigration check travelling airside between the terminals, but I would not advise you trying to go to the other terminals unless you are flying from them.