Postgres 12

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SELECT string_agg(CASE ceil(random() * 4)
                  WHEN 1 THEN 'A'
                  WHEN 2 THEN 'C'
                  WHEN 3 THEN 'T'
                  WHEN 4 THEN 'G'
                 END, '') AS dna
FROM   generate_series(1,100) g  -- 100 = 5*N
GROUP  BY g%5;

dna

ATAGGCTATCATTCAGCTAG

GATGGGAAAATCGTCTGGGT

GCACCTACCTGAAGAACTGA

CTACGTGTAAATCATATGGG

AGCCCGAGTCGGAGGTCCCA

PREPARE dna_length(int, int) AS
SELECT string_agg(CASE ceil(random() * 4)
                  WHEN 1 THEN 'A'
                  WHEN 2 THEN 'C'
                  WHEN 3 THEN 'T'
                  WHEN 4 THEN 'G'
                 END, '') AS dna
FROM   generate_series(1, $1 * $2) g
GROUP  BY g%$1;
EXECUTE dna_length(5,20);

dna

ATCTTCGACACGTCGGTACC

GTGGCTGCAGATGAACAGAG

ACAGCTTAAAACACTAAGCA

TCCGGACCTCTCGACCTTGA

CGTGCGGAGTACCCTAATTA

EXECUTE dna_length(3,7);

dna

TAAACAT

ATGGGTT

AAAGTAT