You will not have access to any airside lounge in T5
I suspect you can use the Air Lingus lounge in T2
You would potentially have access to the BA arrivals lounge which is landside at T5.
Depending how long your connection is and what time you land you might consider this lounge too.
Assuming this is all on one ticket then its probably best just to take the airside bus to T2 and use the Air Lingus lounge