For my explanation, here 经过 means Pass through (undergo). your understanding is right. After the police learn about it, the man was sentenced for 5 days in custody. but you translated the sentence not into the right word. but based in my English level, I couldn't give an accurate sentence, I try to say" After undergoing the police investigated, the man was sentenced for 5 days in custody. "
经过 can means go through a place or a gate, via a mall,via television or pass through a situation/procedure. undergoing some events. etc. but in chinese meaning, it is a verb and preposition that translates as after or go through and by.... I googled it that said it means that. I just do my best to clarify it. if you have any doubt please let me know.