Do you just put it like
Prologue Present Day
And then Chapter 1 Chapter Title 5 Months Earlier
Or am I missing something?
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You can do it explicitly like you stated or ....
Another method is to incorporate a unique setting and event in both. For instance, the Prologue happens on Bilbo's One Hundred and Eleventeenth birthday and in the first chapter they are planning Bilbo's One Hundred and Eleventeenth birthday party.
The benefit of this method is it builds engagement bevause the reader is arranging the story elements chronologically themselves.
Similar examples, in Prologue, the Challenger or the Columbia disaster is live on television. Then Chapter 1 has first launch of Space Shuttle referenced. The reader puts things together for you without clumsy and boring exposition. Admittedly, this is not 5 months apart, but its an example, for illustration purposes -- disclaimer needed for all those middle children that need to quibble of details and not see the bigger idea being presented.
The linking moments doesn't have to be directly part of both stories, they can chronological -- like Christmas 1942 then the previous 4th of July. Or they can be deeply involved like the Prologue is the Seven Days War and the first chapter is Generals planning thier attack.
The linking event is chosen so it doesn't feel obviously forced, it should feel natural to the story and the characters or other events.