Mares can and do carry foals at this age, but they are usually "professional" broodmares - mares that have been bred back year after year.
An older mare who hasn't had a foal for several years may not cycle and bring up a breedable follicle without a LOT of medical intervention. Make sure you understand what the procedures and costs involved are before heading down that road. Those are questions for your vet, and I hope you can find a repro specialist to work with.
I like your mare, but before doing this I think you should ask yourself some hard questions about your reasons for breeding her.
Is she an absolute top of the line sport horse prospect? If she wasn't already yours, is she the broodmare you'd pick to sire a sport horse foal? If you're breeding her for sentimental reasons, because you adore this mare, is that worth the risks of breeding an older mare?
I'm assuming that you know that this is the most expensive and time consuming way to get an event prospect, that choosing a 2 or 3 year old or even a yearling is a much, much less expensive way and much shorter way to get what you want.
All that said, first things first. Get the vet out and have a breeding exam and a uterine culture and a blood draw. Find out if the vet thinks she's breeding sound. The vet may want to monitor her and find out if she's cycling this spring, so he may want to have her teased by a teaser stallion and then palpate her when she shows in. Alternately, he can manipulate her cycle with hormones and see if she brings up a breedable follicle.
If the vet thinks this is doable and wise, then I assume you'll be looking at stallions and shooting for a breeding early next year, you've pretty much missed breeding season this year.
Whatever you decide to do, good luck.