Hi, M.. My two cents is this: She is five, her brother is 3, her dad is overseas. She doesn't know where Afghanistan is, but she knows it's "far, far away", right?
She gets to see her brother stay with you when she has to separate from you both and be alone at school. Since this just happened out of the blue, I'd call it a phase.
But it's fear, nonetheless.
I grew up with a dad who travelled to the middle east in the early 80's as a medic. He was on that stint for 4 years, home every 8 months. I am the oldest and I, too, wanted to retreat in the middle of this "routine" suddenly and just hibernate at home. Home, in my mind, was a shelter. A coccoon. I was in the 4th grade. So, hell yeah - totally reasonable to feel that way in Kindergarten. And unless you know for a fact that she's socializing with a kid or two in her class who ALSO has a parent overseas, can you imagine how "out of place" she may feel? Watch her face when she sees a "dad" pick up one of her classmates; she may not be sad or show emotion, but she may be watching them, even still. Get in her brain, stand in her shoes.
The dynamic in your household must, in some way, call for your daughter to be a bit of a helper for you, right? Even little things, like helping with her baby brother?
Go that route even further. Make her feel like an important cog in the wheel of your family. She "needs" to go to school because "you guys are all learning to read now!" and "you guys are helping other kids learn how to tie your shoes, count,..." etc, etc... parlay that into, "I'm hoping you can go every day and then come home and help ME teach your brother these things....." See where I'm going with this? School can be "her job" (and in the long run, will be).
Don't cave in. And homeschooling - yes - is great; actually have a cool, albeit small, homeschooling community in our neighborhood; very organized. But right now, your oldest child may need that social environment more than you realize. And even though she's pulling away from it right now, it "is" familiar territory to her. Don't move stuff around on her right now.
You're doing the right thing pursuing the route of asking her about school. If something is happening, someone's picking on her... any of that, it explains A LOT. But she may not be one'a those kids that "volunteers her daily schedule" (two of mine clam up, one of mine is Little Miss, "Okay, today at 10:17, my friend Olivia got glue on her shoe.....") In which case, you'll have to play the process of elimination game. Keep her hands busy, interrogate her when you guys are rolling play-doh or coloring together. And just go down the list, "So, how was today? Did you play with so-and-so? Did you get to be line-leader for bathroom break?...." listen to her tone, watch her eyes... put the pieces of the puzzle together. Your instincts will get to the bottom of this!
Good luck and hugs to your little ones!