A baker can decorate 5 cakes in 3 hours. How many cakes can he decorate in 4 days if he works 9 hours each day?

The baker can decorate 5 x (9 / 3) = <<5*(9/3)=15>>15 cakes in a day.

Therefore, he can decorate a total of 15 x 4 = <<15*4=60>>60 cakes in 4 days. Answer: \boxed{60}.