I’m afraid you’re not automatically entitled to reduce your hours. People are allowed “reasonable” time off for family emergencies, such as someone suddenly being admitted to hospital, but routine carers’ duties wouldn’t count as an emergency.
That doesn’t mean to say it’s not worth asking, however.
I think a difficulty you will face is that if you only want to reduce by a small amount, it’s actually harder to find cover for those hours you’ll be dropping. Nobody - or very few people - are going to apply to work just one hour a day, between four and five. It’s inconvenient, and not worthwhile. Therefore, in practice, the likelihood is that your work either won’t be covered for that period each day (which may or may not matter, depending how critical your role is), or will have to be covered by colleagues, in addition to their own work - which might not go down too well. So in a way, it would be easier to accommodate if you wanted to reduce more. If you switched to, say, mornings only, it would probably be relatively easy to find someone who would like to work only afternoons. Similarly, if you switched to a 3-day week, there’s almost certainly someone around who would like the other two. But five hours at just one hour per day would be hard to fill.