I have a connection to Oviedo from Terminal 5 later.
Do I need to go past customs before my Oviedo flight?
Arrivals from Dublin at Terminal 5 can only be handled at gates A22 and A23, at the north end of Terminal 5A. This is because Dublin arrivals are unique: they do not need a passport check but do need to go through customs if entering the UK and do need to go through security again if connecting.
If your plane has to park elsewhere, then you will be bussed to the special Dublin entrance at 5A.
Since you are not entering the United Kingdom you will not need to pass through UK Customs, but you will need to clear security. You should follow the purple signs to Flight Connections.
However, most people find that from Dublin it is quicker to exit via the baggage hall and then go upstairs and back through security rather than pass through Flight Connections security. But if you are not familiar with the airport you should just follow the purple signs to connecting security.
Domestic flight arrivals use T5A which is the main building, not a satellite. This is because their passengers have to bypass Immigration and the satellites don't have separate routes back to the main terminal for this. If your plane physically arrives at B or C you'll be bussed to A, and you might also arrive at a remote stand and need buses anyway.
Long haul departures can use any of A B or C, though B or C are most likely.
There aren't specific gates permanently alliocated to individual flights, I doubt if even BA themselves know more than a few hours ahead which gate will be used.