How to know what size of needle I need

I want to start knitting so bad and I already bought my first needles but I'm not sure in the yarn I have is the correct size for it(? For more context, I crochet already, I have a bunch of yarn all over my house but the ones I use the most go perfect with a 4 mm hook size, so now I'm wondering if it's going to work well with my 5.5 needles or if I should find a thicker yarn. Does 5.5 means 5.5 mm like in hooks? Or it's different? How can I know?