Hitting the Infinite Frog

A frog is at a point on a number line which consists of only positive integers. Starting from that point, the frog is planning to jump 5 units to the right at a time. Hunter Jim, who knows neither the frog's current position nor its planned pace in a jump, wants to devise a strategy to shoot down the frog. He and the frog take turns, i.e. the frog jumps, he shoots a number, the frog jumps, he shoots a number, and so on.

With the optimal strategy, will he be able to hit the frog eventually?

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