Heathrow T5 to Newbury

Bus/train will be 1h50

Elizabeth line to Paddington then train would be 1h30

Generally it is suggested that it's an hour from flight to exit at Heathrow - can be less and can be more, but it's a safe average for timings. There are fully flexible tickets available too

One other alternative is to take the Elizabeth line 1 stop to Hayes & Harrington, transfer to a different Elizabeth Line train to Reading, and then lastly a train to. Newbury. This won't save you any time over the bus but it's an alternative.

But, honestly, if you will be staggering off a plane, take either the Elizabeth line or Heathrow Express to Paddington and then a train to Newbury.

Or

Bus to Reading, then train. The bus is just outside T5.

None of this has to be pre-booked and both (if rail/air coach to Reading then train) or all (if any of the various train routes) sectors are very frequent, so it doesn't matter how much time it takes to clear the airport, which was your question.
Just take the next available transport on whatever route you opt for. Pay on the spot.

The railair coach to Reading is now rather more expensive than it used to be, particularly for a one way ride, and less frequent at twice rather than three times an hour. Still sometimes its convenience trumps costs. Book the bus separately. It costs somewhat more to buy from the driver than in advance but is not essential.

Thank you all very much. This is all quite reassuring.

Depending upon how tired you think you will be, you could do a splurge and take a car service directly from Heathrow to the door of your AirBnB. We have used Blackberry Cars and have been pleased with their service.
https://www.blackberrycars.com/distance-transfers/heathrow-distance-transfers/taxi-newbury-heathrow-airport/
Heathrow to Newbury £119, according to their above page.

Holy cow, Rebecca, that's tempting!! Expensive, but tempting. Around $150 at today's rate... Hmmm...

Some splurges are worth it. Not urging you one way or the other, just wanted to give you one more option.

Oh, I totally agree. I had no idea that hiring a ride was an option! It might be nice to know that all I have to do is find the door where the driver's waiting. I'll be doing plenty of training and tubing and coaching on my own since I'm giving myself a few days before and after the tour.