Can you get pregnant with semen on your hands and after five to ten minutes go to the bathroom and wipe before washing your hands?

I am not an expert by any means but as far as I understand, sperm don't live for very long outside the body, and they don't even travel that well inside the body, in fact they rely in the semen to travel inside the vagina. So I expect that while it may not be impossible, it would be very unlikely that any could (a) survive for ten minutes on your hand; and (b) somehow make it right through the vagina from the outside.