Is it correct to say "I'll reach there in about 5 minutes?" Is "in about" correct in this sentence?
This is perfectly fine. I suspect you might be confused because you are seeing "in about" as a linkage of two contradictory prepositions, meaning something like "inside outside." But those aren't the meanings here. See it this way instead: "in" is used to indicate a period of time ("5 minutes"), and "about" in this case means "approximately." So the sentence is, "The period of time it will take me to reach there will be approximately 5 minutes."