>(SELECT code1 as code FROM test1 where code1 between 'c555' and 'd998' )
>UNION ALL (SELECT code2 as code FROM test1 where code2 between 'c555' and 'd998')
>UNION ALL (SELECT code3 as code FROM test1 where code3 between 'c555' and 'd998')
>UNION ALL (SELECT code4 as code FROM test1 where code4 between 'c555' and 'd998')
>UNION ALL (SELECT code5 as code FROM test1 where code5 between 'c555' and 'd998')

>　そこで、これらの結果から、合計数５のみを求め、表示したいのです。

これでどうですか。

SELECT SUM(IF(code1 between 'c555' and 'd998',1,0))
     + SUM(IF(code2 between 'c555' and 'd998',1,0))
     + SUM(IF(code3 between 'c555' and 'd998',1,0))
     + SUM(IF(code4 between 'c555' and 'd998',1,0))
     + SUM(IF(code5 between 'c555' and 'd998',1,0))
    AS total_count
  FROM test1

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