On the existence of Weierstrass points whose first non-gaps are five

LetH be a numerical semigroup, i.e., a subsemigroup of the additive semigroup N of non-negative integers whose complement N/H in N is finite. Leta be the least positive integer inH. Then we show that ifa=5, then there exists a pointed complete non-singular irreducible algebraic curve (C, P) such thatH is the set of integers which are pole orders atP of regular functions onC/{P}.