I got confused by the sentence:
An investigation took place,and five months later Dan was exonerated and returned to active duty.
I wonder whether a comma may(or should) be inserted after the word "later"
It's a matter of style. If you set off "five months later" with commas, you've got three commas in a short space. Whether it makes the sentence easier to read is not obvious:
An investigation took place, and five months later Dan was exonerated and returned to active duty.
A newpaper or a journal may have a style it prefers. Newspapers are inclined to eliminate commas when they can, because they take space. A comma can cause a paragraph to take up an extra line of type, and a few lines of type is a paragraph that can't be published.
A copy editor of a book often applies a consistent style throughout a book, although it may be based initially on the author's style. A more open (few commas) style still allows the use of commas essential for meaning and ease of reading.
Just because a phrase can be set off by commas doesn't mean it should be, or that it's unnecessary information; it just means it's not essential to the syntax of the sentence.
An investigation took place, and, five months later, Dan was exonerated and returned to active duty.
This would be a better way to write. Since five months later is unneeded information, you can use commas to offset it from the rest of the sentence.
If you're doing this, you need to place a comma at the end of later. Nonessential words or phrases must be closed off.