Question

He was only 27 in 1963, but he (teach) already at Galton University for five years.

Answer 1

He was only 27 in 1963, but he had already been teaching at Galton University for five years.

for five years - указывает на продолжительность действия (Continuous)

already - указывает на перфектное время (Perfect)

was - прошедшее время, для согласования и 'teach' должно стоять в прошедшем (Past)

Значит, нужное время - Past Perfect Continuous.