You're right about not using the rake. The roots haven't really taken firm hold in the soil yet. At 5", it should be mowed. I would go ahead and mow but bag the clipping and the leaves at the same time. You can use the bagged clippings/shredded leaves in the spring for mulch or compost them down. Yeah, some of the new grass might be slightly damaged by the wheels of the lawnmower but just take those turns easy to minimize damage.
