In this paper we consider divisor classes on elliptic modular surfaces S(n) and their associated linear systems. A principal role is played by divisors I which have the property that nI (resp. n/2I) is linearly equivalent to the sum of the n sections if n is odd (resp. even). Our main result is the description of four different projective realizations of S(5). Some results concerning S(3) and S(4) are also discussed.