A hand pump can push as far as your arm is strong enough. It just can't pull more than about 25-27 feet. This is because atmospheric pressure is just about the same as the pressure at the bottom of a column of water 30' tall.
Once you have a column of water that's almost 30' tall, atmospheric pressure can't lift the water any higher.
As for 5GPM, with a head pressure of 30', (that's 5' pulling and 25' pushing), A 1/4hp pump would work. A person supposedly can produce around 100 Watts continuously, a HP is 746 Watts so if you're in good shape, you could probably pump 2 to 2.5 GPM.
An Olympian might pump 5GPM for the first minute.