> The second sentenxe doesn't follow the first - it's a flavor of Zeno's paradox, after 5 years, you'll be left with 4/5 x 4/5 x 4/5 x 4/5 x 4/5 of the original batch.

You made a mistake: it's not that 1/5 of the computers spontaneously break every year. It's that 1/5 of the students treat their computers roughly.

Assuming that laptops get collected over the summer and re-distributed each year, you should actually expect that 100% of each tranche of laptops would need to be replaced every 5 years.