That certainly does look like a TR5T !
The
"History" page on this Forum refers to the TR5 as being manufactured from 1949 to 1958,
and the image they have looks like a completely different machine, however the next model TR6,
( 1956 - 1970 ) which does not have a Photo on the History page, looks a lot more like the TR5T -
Perhaps the TR5T was introduced as the TR5 was being phased out, and replaced by the TR6 ?
Here's a picture "borrowed" (

) from Mr. Google of the TR6 :
