Is it right to be separated and sleeping with someone else after only 5 months

If the separation is permanent, why not!!

You are asking the people on here to answer that question for you?

I believe it is a question you need to answer for yourself.

What does your gut say?
How do you feel about it?

Sounds like jumping out of the skillet into the fire.

Anyone who is willing to date you while you are still separated is willing to risk being a rebound and that kind of desperate is not a good sign.

It is not to say that separation is not a common first step towards divorce but never a guarantee.

The fact that a person has picked a person they need to divorce is a choice I think requires some soul searching or self reflection before they move forward. VERY rare that marriage is not a choice and someone who demonstrates to you that they make bad choices and take no time to evaluate how to avoid repeating that mistake would give me pause.

That does not even take into account being walking wounded ; especially if they divorce was not their choice. Personally I want someone who at least starts the relationship wit the past finished and standing strong. I don't need "work in progress " romances.

Maybe what is right for me is different for others but if the question is if it is wrong those would be my reasons why. It is always a personal choice to pick poison.