yes the answer is 9!/(4!5!) . In order to reach his destination he has to take 9 steps , 5 upwards and 4 towards right. He may do so in any possible manner as he wish.
Now , you have to basically arrange those 9 elements knowing that 4 of them belongs to one category and the other 5 to another .
Hence answer : 9! / (4! 5!)