You want to select all the records except thos records with a forumid of 5,18 and 19? Is that right? You need to use logical AND not OR. If I am correct that sql statement will be returning all the records. Right?
With logical OR only one of the conditions needs to be true for the result to evaluate to true. So if you construct a truth table you can see that all records will evaluate to true:
$myselect = "SELECT *
WHERE forumid <> 5
AND forumid <> 18
AND forumid <> 19
ORDER BY lastpost DESC
Hehe, I don't know if that looks like a table to you - it looks ok in my browser.
| <>5 | <> 18 | <> 19 | <>5 OR <> 18 OR <> 19
5 | F | T | T | T
18 | T | F | T | T
19 | T | T | F | T