Train from Birmingham Int'l to Heathrow terminal 5

What the routing will be is the connection from Euston to Paddington is not showing as a specific train, just giving you time between your arrival at Euston and departure from Paddington. In any event I would take a Northern line train from Euston to Tottenham Court Road and then the Elizabeth line to Heathrow, rather than connecting through Paddington.

Thank you so much for the advice. Tottenham Court Road does appear to be the easier of the two.

alternatively train to Reading and Railair bus to airport https://www.railair.com/

I was also going to suggest taking the train to Reading and then getting the RailAir coach. The train to Reading is direct. No changes. The coach stop is right outside the train station. Less transfers and walking.

There is also the hourly Avanti train from Birmingham International to Watford Junction and the hourly Rail/Air bus from Watford Junction, granted that one only gets you to Terminal 2/3 for free transfer to 5.
The service bus 724 also does the run in almost the same time- so a combined 1/2 hourly frequency.

Don't book that one as a through ticket because that Rail/Air now only costs £3 - paid on the day or on their own website.

the Watford idea also gives more chance of getting a decent discount on the train tickets tickets than Reading, but slightly less convenient because most of the Watford buses only serve the central bus terminal at Heathrow