Creating a Character Array with a Certain Number of Vowels and Consonants (Java)

I am trying to create a program that outputs ten lowercase letter characters - five vowels and five consonants. In order to do this, I have started by creating a char array with a range between 'a' and 'z' called letters[] with size 10. Once the array is filled, I will print the output with the use of a format string containing everything in the array.

My question is, how would I make the program output exactly five of each type (and keep the order of the characters printed completely random)? I have considered using the switch statement with a case each for consonants and vowels, but my ideas so far seem over-complicated and inelegant.