Let W = {w1, . . . , wr} be a set of positive integers, λca positive integer, Λa= (λa(1), . . . λa(r)) an r-tuple of positive integers, and Q = (q1, . . . qr) an r-tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code, (n, W, Λa, λc, Q)-OOC, for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal (n, W, Λa, 1, Q)-OOCs with unequal auto-correlation constraints for W = {3, 4} and {3, 5}, while little is known on optimal (n, W, Λa, 1, Q)-OOCs for |W| ≥ 3. In this paper, we focus our main attentions on (n, {3, 4, 5}, Λa, 1, Q)-OOCs with Λa∈ {(2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}. Tight upper bounds on the maximum code size of (n, {3, 4, 5}, Λa, 1, Q)-OOCs are obtained, and infinite classes of optimal (n, {3, 4, 5}, Λa, 1, Q)-OOCs are constructed.