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?

In 1 day, the baker can decorate 5 cakes/hour x 9 hours/day = <<5*9=45>>45 cakes

In 4 days, the baker can decorate 45 cakes/day x 4 days = <<45*4=180>>180 cakes. Answer: \boxed{180}.