I work in HR and we do see these requests from time to time - mostly our managers come to us for advice as to what they should do...

If I were advising a manager on your situation I would suggest to them that it would be beneficial to them to allow you to reduce your hours to 4 days per week so that they can plan around your days off rather than having unpredicted absences.

My HR role would then also require me to ensure that the employee had sufficient leave to cover the period and if not ensure that the employee knew of this before hand.

HTH - all the best with your manager and employer