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Make another page and modify the query with "LIMIT 5, 5". You could take a page value from a URL query in order to change the limit as well, so if you're on page 3 you would want "LIMIT 10, 5", etc.
I think you could use OFFSET in your query, though this has some performance issues if you start trying to 'offset' from large numbers (I think adding an ORDER BY clause would help, otherwise MySQL presumably just has to wade its way through x amount of rows until it knows where to start from.)
The main use of LIMIT and OFFSET is to generate the kind of "Now showing results x of x" pagination you get with search engines. The following tutorial shows write to write a script that does this and might be what you're looking for:
If you want to use the same script to either show new or old posts you need to send a $_GET[] value back to the script (so this part of the script is recursive in that respect).