Select values from a list that are not in a table

A temp table is the best solution, but if not possible then you can fudge a temp table by selecting constants and unioning them together.

Using this solution you can do the following:-

SELECT i
FROM 
(
    SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 6 UNION SELECT 7
) AS mylistofids 
LEFT JOIN mytable
ON mytable.id = i
WHERE mytable.id IS NULL;

You can also generate a massive range of numbers (assuming that you are dealing with integer ids) by cross joining ranges of numbers. Then just pick the ones that are in the IN clause:-

SELECT i
FROM 
(
    SELECT units.i + tens.i * 10 + hundreds.i * 100 + thousands.i * 1000 + tensthousands.i * 10000 AS i
    FROM (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS units
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS tens
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS hundreds
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS thousands
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS tensthousands
) AS mylistofids 
LEFT JOIN mytable
ON mytable.id = i
WHERE mylistofids.i IN (1, 2, 3, 6, 7)
AND mytable.id IS NULL;