You can change the day of the Amazon Day Delivery to when it suits you.
I use that sometimes as it means I get my order when I'll be home.
That's exactly what it is. You can set a preferred day of the week, and Amazon will default to delivering on that day instead of next day. In your case it thinks your preferred day is Saturday.That is not what I was writing about.
The item is advertised on Prime next day, but on checkout you have two options: No Name Next Day (I suspect this is Hermes) & Amazon 5 days later.
That's exactly what it is. You can set a preferred day of the week, and Amazon will default to delivering on that day instead of next day. In your case it thinks your preferred day is Saturday.