Achilles would have to move 10 meters to catch up to the tortoise, but the tortoise would already have moved another five meters by then. Achilles would then have to move 5 meters, where the tortoise would move 2.5 meters, and so on.
To catch up to the tortoise, Achilles needs to advance 10 meters; however, during this time, the tortoise will have moved an additional 5 meters. Subsequently, Achilles advances another 5 meters, but by then, the tortoise has already moved a further 2.5 meters.