I arrived at T5 on Sunday afternoon a week or so ago. Sudays can be pretty busy so I was dreading it. However, queues for both EU and non-EU passports were reasonable (I'd guess 15 mins and 5 mins max, respectively), and thankfully IRIS was working, though I thought it had been discontinued.
Then - and this was the really surprising thing, based on my previous experiences - despite only having spent about 5 mins in immigration, and despite the flight having arrived at the C gates, when we got to the baggage carousel, bags from our flight were already arriving.
This doesn't mean that LHR can't be hell on earth, but it shows that it can work.