To determine the number of stitches to cast on when using 5.5mm needles instead of 9mm needles, you will need to calculate the gauge difference between the two needle sizes. Start by knitting a swatch using the yarn you plan to use and the 5.5mm needles. Measure the number of stitches per inch/cm in your swatch.
Next, knit another swatch using the same yarn but with the 9mm needles. Measure the number of stitches per inch/cm in this swatch as well.
Calculate the ratio of stitches per inch/cm between the two needle sizes. Then, multiply this ratio by the desired width of your project to determine the number of stitches to cast on with the 5.5mm needles.
Remember that the resulting number may be a decimal, so you may need to round up or down to the nearest whole number to ensure your project turns out as desired.