Fastest way to travel from Heathrow Terminal 5 to Swindon, in Wiltshire by train or bus

My feeling is the rail/air bus to Reading station then the train onwards.

On the way back you could instead use the direct National Express bus at 1315 to Heathrow Central Bus Station, arrive 1445, then tube/Elizabeth Line/Heathrow Express free transfer to Terminal 5.
That doesn't work outbound as there is a service interval from 1500 to 1800.
That bus starts at Swindon.

There is little or no time difference between the above rail/air route and the 3 train route- Heathrow to Hayes and Harlington, H and H to Reading, Reading to Swindon.

The Rail Air Bus runs every 20 minutes and takes 45 minutes from Heathrow to Reading. The train is every 30 minutes and also takes 45 minutes (35 from Hayes and Harlington).

Train throughout is £44.50 TO Swindon at that time of day, £34.10 on the way back, via rail air it is £50.50 on the way out, £43.50 on the way back- or the return fare would be £82.

So best is pretty subjective. No knock out winner IMO.

National Express next Tuesday is £15.70, and this Saturday to Swindon on the 1800 service is £18.90

unless your friends would like to meet you off the plane and take you to their home...

That's probably what I would do, but I'm not them...

A couple of nice things in and around Swindon