Upvote:-3
If the hotel is inside the boarding area, it might not be necessary do inmigration. To move from terminal 3 to T5, there are free trains every 15-20 minutes. You can get further information at: https://www.heathrow.com https://www.airportsdata.net/europe/united-kingdom/airports/london-heathrow.php https://en.wikipedia.org/wiki/Heathrow_Airport
Upvote:1
You should leave the airport at the terminal you arrive.
When you have gone through immigration (passport control) and customs ('nothing to declare') you will find signs for the free transport between the terminals.
It is not strange to leave the airport with no more than just a little hand luggage. If asked about it, (customs can stop you if they have questions,) just tell them most of your luggage is checked through. There are even people traveling with less luggage than you will have, without hold luggage.