A21-23 normally

It is about the nearest gate there is at T2, you DO NOT need a boarding card to get through connections at T2, Aer Lingus has a desk just after the passport control area who will sort it out for you.

If you arrive into T5B as you head down stairs for the train to T5A keep an eye out as there is a hidden stop for the T5-T2 connecting bus on the ground floor, find the Heathrow staffer in purple and tell them you want T2 and they will radio the bus to make a request stop

Saves a few minutes, if you arrive T5C or T5A ignore above.

My best time from T5B gate to A21 including a pat down at security and collect a new boarding card is sub 30 minutes, the longest part is the bus ride. T2 transfer security is separate to main security and I've never seen it busy even during normal operation. If this is planned for a time when normal operations might be in place again, I typically book a long connection and when presenting myself at T2 EI desk the agent will offer an earlier flight if HBO (and if you have status they sometimes can redirect checked luggage to make it happen)