Two vowels can be selected in 5C2 ways.
Three consonants can be selected in 17C3 ways.
∴ 2 vowels and 3 consonants can be selected in 5C2 × 17C3 ways.
Now, each group of 2 vowels and 3 consonants can be arranged in 5 ! ways.
∴ The total number of words = 5C2 × 17C3 × 5 ! = 816000.