lhr – Heathrow Airport: Terminal 2 to Terminal 5, can you transit without visa? (conflicting answers)

Yes you will need a visa, specifically the Visitor in Transit visa, but you may have a chance at transit-without-visa (as you fit some of the criteria there) although I wouldnt recommend just chancing it.

Being that your flight leaves the next day, you cannot stay in Heathrow terminals overnight as they close to passengers and there are no airside hotels at either terminal – this means that even though you can transfer airside between Terminal 2 and 5, you need to enter the UK to stay at a hotel before either of those terminals close for the night.