You should be in luck, as from the 9th Jan next year, the minimum connection time T5-T5 International-International is going up from 60 mins to 75 mins.
There are some exceptions to this general increase (though perhaps only domestic) and we'd need exact details to be 100% sure, but looks like you now fall below MCT, so will need to be rebooked (at no cost). It's not uncommon to be initially rebooked on flights that don't meet MCT, there is a later pass that sweeps up such bookings and marks them as invalid.
If you are coming in to T2 on Aer Lingus, MCT is 90 mins so you are certainly below that now.
If you are coming in to T5 on BA, MCT is currently 60 mins, so is a legal connection at the moment, but will become 75 mins on Jan 9th 2024 at which point it ceases to be.....