"They finish school at 5 today."
...unless they wanted the English sentence to mean that they finish the term at 5 today? (And putting ‘today’ at the start of the sentence puts too much emphasis on it?) ... Or maybe the sentence I gave implies that today is unusual and the Chinese doesn’t? Happy to be corrected if it just sounds wrong. Will see if it changes.
This is by no means a grammar explanation, just my interpretation of the word, and how I have memorised it. 放 means to release, to free, to let go, to put, to place, to let out. So, in this particular sentence you can imagine "studies/classes are being released/let go/let out" therefore meaning finished. "What time did class let out?" "Today they were let out at 5."