K (ngn/k), 57 47 46 54 bytes

{`prng@0;,/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}

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Down 1 byte thanks to ngn

Takes inspiration from the PHP answer. This one now outputs random words at each call, with the cost of 8 extra bytes.

Explanation:

{`prng@0;,/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5} Main function. Takes no input
                                                   !5  Generate a array with range from 0 to 4 ([0..4])
                                                  '    For each number...
           {                                     }     Execute a function that...
            (1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"      Chooses one random consonant, followed by one random vowel
         ,/                                            Joined each of these strings together
 `prng@0;                                              Use current time to set state of randomness (Thus allow random words)