When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to \(0^{}_{}\) and is the same as that of getting heads exactly twice. Let \(\frac ij^{}_{}\), in lowest terms, be the probability that the coin comes up heads in exactly \(3_{}^{}\) out of \(5^{}_{}\) flips. Find \(i+j^{}_{}\).

(第七届AIME1989 第5题)