Thanks for all the replies. Actually landed half an hour early at T3 tonight, so made my way over to T5 to chance my arm. Was told to go to zone E and made it there at 10.01pm. No issue checking bags for tomorrow morning’s flight, which is very handy!

I don’t know how true this is, but the check in agent said Zone E is open “all night”. He personally was on duty until midnight. I appreciate this contradicts KeaneJohn’s experience above, but a good result for me!