He has grown up 5cm.

Last month he was 165cm height. This month he is 170cm height.

He has grown up 5cm.

Does this sentence make sense?[/b]

Last month he was 165cm in height. This month he is 170cm in height.
Alternatively, you could say: “he was a height of 165cm”, though if you are speaking about a human then really ‘height’ is not the best word to use at all:
Last month he was 165cm tall. This month he is 170cm tall.

He has grown 5cm.