Another word for Raise and Lower
Solution 1:
He lifted the dumbbell to shoulder height and then pumped it to the arm's full extension five times.
Bafflingly, I am not finding the relevant definition in any dictionary. But pumping involves a repeated back and forth, or up and down, motion. Literally speaking, the purpose is in order to get a system to a certain state, for example, to get enough air into a bicycle tire.
Think of pumping the brake when you hit an icy patch of pavement.
Solution 2:
The word you are looking for may be repetition.
From Oxford Dictionaries:
repetition: a training exercise that is repeated, especially a series of repeated raisings and lowerings of the weight in weight training.
Note: I acknowledge that @bib mentioned repetition (and rep) in a comment on the question. I didn't see it. I work with some weightlifters and repetition came immediately to mind.