I guess the answer to your question depends on what size garment you are trying to make. If you need the smaller size, then, of course, you’ll need to use a larger needle to get the right gauge. If you want to make a larger size, you could use the size 5 needles and follow the smaller sized pattern (since your gauge is more stitches per inch than what is recommended).
Personally, though, I’d try to get the right gauge by using a larger needle. That way you’ll have a pretty good idea of the final size of the garment.
Also note that in [U]most[/U] patterns, it’s more important to get the number of stitches per inch than the number of rows per inch. Most patterns allow you to add rows until you hit the right length.
Can you give us a name and/or link to your pattern, please?