A 5.0mm would be an H-8 hook.
You should use a size J/10 crochet hook for a project that requires a 6 mm crochet hook.
You should use a crochet hook that is labeled as 5.00 mm for the project.
A 0.9 mm steel hook is about a US size 13.
For a project that requires precise detailing, like using a .5 mm crochet hook, you should use a small-sized hook to achieve fine and intricate stitches.
A U.S. size 7 yarn hook is 4.5 mm. http://www.crochetmagazine.com/hook_sizes.php
Projects that are best suited for a 2.5 mm crochet hook size are typically intricate and delicate items such as lacework, amigurumi, and fine garments like shawls or baby clothes.
A size "C" crochet is generally around 2.75 mm in the United States. There isn't really any specific standards regarding crochet hook sizes, different manufacturers made their hooks in different sizes, and that pretty much still is happening today.
that would be a size P crochet hook
00 is a steel hook size. Manufacturers vary in their mm sizing. I found 00 hooks listed as 2.75 to 3.5mm If you have a particular hook and you need to know the mm sizing of it, I suggest you purchase a Crochet Hook Size Gauge Tool. The knitting needle ones do not give accurate sizing for a crochet hook. Annie's Attic sells these and I'm sure other stores do as well.
In the US, knitting needle sizes are in numbers; crochet hooks use both numbers and letters.
You can use another size that gives you the gauge you want.
The recommended size of crochet hook for working with yarn that is 5mm thick is typically a 5mm crochet hook.