He can choose an appetizer 5 ways.

For each of those 5 ways to choose an appetizer,
he can choose an entree 6 ways.

That's 5*6 = 30 ways he can choose an appetizer and an entree.

For each of those 30 ways to choose an appetizer and an entree,
he can choose a dessert 3 ways.

That's 30*3 = 90 ways he can choose an appetizer, an entree,
and a dessert. 

Answer and how to get it: 5*6*3 = 90 ways.

Edwin