I would not be concerned about someone taking prednisone having sex and passing it to their partner. Are you allergic to prednisone for why you are asking?
The risk of having close contact with someone when you are on a prednisone prescription is to you, not to the other person. Taking prednisone can make the person taking it more prone to getting infections. I haven't seen any risks to the partner noted in the literature, just risks to the person taking the medication. How long will the prescription run? Is it just a 5-day prescription or something longer?