HBO T5-T2 connection time and can I stay airside?
 

You can certainly stay airside, but clearly whichever route you take you’ll have to re-clear security. T2 is pretty good, on the whole, and certainly much better than T5 in transit security. For that reason, I’d be inclined to take the airside buses rather than have to wait for the HEX or, probably the quicker option, the tube (which will land you much closer to T2).

This is clearly a fairly tight connection, but there’s no conformance at T2 as far as I know, and EI will usually depart from the A gates.

Sure you can stay airside and take the buses, but you won't have a connection. Moving between (and sometimes within) terminals at LHR is never the easiest exercise, and time is quickly eaten up. If you are late to board your next flight (ie because your Madrid inbound was 30 minutes late - not unusual at LHR), you may find yourself having to buy a new ticket to BHD.

Airside would be quicker by a good 15 minutes. If going landside the tube is better since it's right by T2 whereas HEX is a bit of a hike. The T2 Flight Connection centre is quicker than the T5 equivalent too, and as with T5 there are biometrics involved after the UK + Ireland passport check. You don't even need a boarding pass, you can collect that from T2 if necessary.

That's certainly a risk worth highlighting however on a 1 hour 40 minute connection then you are probably safe with a delay up to 45 minutes. It takes about 30 minutes to get from T5 to T2 airside all told, it's quicker than getting through T3. EI starts boarding earlier than BA, and will leave 15 minutes early if they can, whereas BA won't leave more than 10 minutes early.