You start with 5sts and the pattern wants you to increase 5 times for a total of 10sts. That means m1, k1, m1, k1, m1, k1, m1, k1, m1, k1. You can use a m1 for the increase as suggested
That'll use up the 5 cast on sts so you won't have extra sts hanging out on the right needle.
That's such a lovely pattern, particularly at this time of year. Our dogwoods are in bloom just now and they are heavenly.