I want to take a 5-day well-needed getaway. When and how should I break it to Mom?

If at all possible start by having them come in 1 or 2 days a week to give you a break and so they get to know the caregiving side to this and it will give your Mom a chance to know them as caregivers.
The first time they step in to do what needs to be done stay with them, the next time go out for a few hours then time after that go for longer then go for a full day.
You will be able to see how things go and if your brother and his girlfriend have any problems.
If they have problems ask them to try to figure it out without having to call you. You and they will realize there is not much that would be considered an "emergency" and as the saying goes....."don't sweat the small stuff..and it is all small stuff"..
Once Mom gets used to having them come in and help out you could tell her that you are going to go away for a while but depending on where she is cognitively she may not retain what you are telling her and if this is something that might upset her it is not worth getting into.
The day you leave, have the car packed, and make it as simple as possible, don't dwell on the length of time you will be gone, time has little meaning. Leave with a hug and a kiss and I will see you later.
She will be fine.
You will have to deal with all sorts of stuff...in your mind..just try to relax and enjoy yourself. You will come back with a fresh perspective.

You might consider not telling her at all until the last minute. Get the car packed when she's napping or distracted. When brother and girlfriend arrive, greet them enthusiastically and visit a bit. Then you might say casually and brightly, "Mom, Husband and I are taking a little road trip for a few days. We were hoping you you could keep Brother and Girlfriend company while we're gone!" And leave pronto! If she does ask to go with you, you might say, "Oh, Mom, we're celebrating _____ (anniversary, whatever) and just need a little getaway! We'll see you in a few days! Bye!" And skidaddle!

First off, you're doing the right thing. Take that break and get respite. It's vital. As a hands on caregiver......I can't imagine how exhausted you are. It takes much mental labor to care for a person who has dementia, plus physical labor.

It likely depends on how far progressed she is. Does she have much short term memory? In retrospect, I wouldn't have told my LO anything upsetting until the last minute, because she was would just obsess, worry and cry. Then, she'd forget and it would start over later. Many people with dementia are not able to process the information, get used to the idea and accept it, so, I'd not plan on that happening. I'd ensure the respite caretakers are prepared for her to repeatedly ask for you and what they might say to comfort her.

My LO did better when told that I was at work. She got that and seemed okay with it. Anything else worried her.