To convert a pattern with 9mm needles and 56 stitches cast on to 5.5mm needles, you can use the following formula:

New number of stitches to cast on = (Desired needle size stitches) x (Original number of stitches) / (Original needle size stitches)

New number of stitches to cast on = (5.5mm stitches) x (56 stitches) / (9mm stitches)

New number of stitches to cast on = (5.5) x (56) / (9) = 33.78

Therefore, you should cast on approximately 34 stitches when using 5.5mm needles to match the original pattern with 9mm needles and 56 stitches cast on.