​How do you phrase it to clients that you’re increasing your rates?

I have a dog boarding business, and this client was one of my first. So she’s been at my LOW end for a few years. I’ve done an increase before of only $5 additional per day. But now I need to increase by $10 per day. She gave me pushback before, and I’m trying to find my backbone, but I’m just nervous about her reaction/losing this client. I’ve checked my competitors, and my new price would still be less expensive.

I want to phrase it well so that it’s clear and understandable, and get advice on how to respond if she gives more pushback.