K (ngn/k), 57 47 46 bytes (Not competitve, yet)

{,/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}

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Down 1 byte thanks to ngn

Takes inspiration from the PHP answer. Because ngn/k's random-related functions are all deterministic, so the output isn't randomly generated (and thus the title).

Explanation:

{""/{(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

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

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

Try it online!

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)

K (ngn/k), 57 47 bytes (Not competitve, yet)

{""/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}

Try it online!

Not particularly concise, but looks pretty well. Takes inspiration from the PHP answer. Because ngn/k's random-related functions are all deterministic, so the output isn't randomly generated (and thus the title).

Explanation:

{""/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}    Main function. Takes no input
                                            !5     Generate a array with range from 0 to 5 ([0..5])
                                           '       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

K (ngn/k), 57 47 46 bytes (Not competitve, yet)

{,/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}

Try it online!

Down 1 byte thanks to ngn

Takes inspiration from the PHP answer. Because ngn/k's random-related functions are all deterministic, so the output isn't randomly generated (and thus the title).

Explanation:

{""/{(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

K (ngn/k), 57 bytes (Not competitive, yet)

{""/{c:"bcdfghjklmnpqrstvwxz";v:"aeiouy";(1?c),(1?v)}'!5}

Try it online!

Not particularly concise, but looks pretty well. Takes inspiration from the PHP answer. Because ngn/k's random-related functions are all deterministic, so the output isn't randomly generated (and thus the title).

Explanation:

{""/{c:"bcdfghjklmnpqrstvwxz";v:"aeiouy";(1?c),(1?v)}'!5}    Main function. Takes no input
                                                      !5     Generate a array with range from 0 to 5 ([0..5])
                                                     '       For each number...
    {                                               }        Execute a function that...
                                        ;(1?c),(1?v)         Chooses one random consonant, followed by one random vowel
     c:"bcdfghjklmnpqrstvwxz";v:"aeiouy"                     Consonant and vowel constants
 ""/                                                         Joined each of these strings together

K (ngn/k), 57 47 bytes (Not competitve, yet)

{""/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}

Try it online!

Not particularly concise, but looks pretty well. Takes inspiration from the PHP answer. Because ngn/k's random-related functions are all deterministic, so the output isn't randomly generated (and thus the title).

Explanation:

{""/{(1?"bcdfghjklmnpqrstvwxz"),1?"aeiouy"}'!5}    Main function. Takes no input
                                            !5     Generate a array with range from 0 to 5 ([0..5])
                                           '       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