Why not! I can give you some suggestions after sort of organizing a hike for charity (Dayhiking the Devil's Path in the catskills to benefit the Brain Tumor Society) Although if you're doing a 5K on public roads, you'll need some official support from the town(s). And if you do that, you'll probably need event insurance and a lot more formal than what I did. Since we were already hiking state land, we didn't need official permission being a dayhike. I would say first, gauge interest, choose a location and date and start early getting permission and insurance should you still chose to go ahead with this. Get volunteers to handle enrollment, membership, the t-shirt stuff, and of course, event day support.
Of course, coordinate with the charity of your choice too. It's a bit of work for one, so I'd suggest if you get enough interest in this, then solicite volunteers. Start small too. If it's going to be beyond VFTT and it'll probably be, you'll need flyers and publicity too.
Don't be surprised if your "small little event" will grow and you might need more support than you're intention.
Seeing your profile being in NH, I'm assuming you're looking at doing this in that area?
Jay