To tag along here and add my 2 cents, competitive is an understatement. As
@WildZoo said, minimum 1 internship, but most end up taking 2 before they are competitive enough to apply for a zoo residency. So on top of 4 years for vet school, that's an additional 6 years of schooling. And THEN!!! The job market is pretty sad for zoo vets. Not only are there very limited spots, but the pay is terrible unfortunately. And the mention of "grad school" after vet school is wrong. Getting a MS or PhD might help if you really want to continue down a more research oriented path, but not required at all.
I've talked to the zoo vets here and a few others from different spots, and have talked to the interns/residents here and none have specifically mentioned a "5" article requirement. Where'd you hear that? Being published definitely helps and is an implied part of your CV on your path to residency, but I've heard no mention of a specific number. If writing (spelling, grammar, etc.) are not your thing and the thought of publishing on a semi-frequent basis makes you nauseous, you might want to reconsider specializing, especially in zoo. Just in the time I've been here, our exotics and zoo vets/interns/residents have written and published several articles. The neat thing about zoo and exotics comes when you're dealing with a case that has never been written about or maybe you establish a drug protocol for a species that's never been recorded. Those types of things greatly benefit the community when you write and publish the details of what you found/did/yada yada ya.
There's also the extended path to getting boarded, but that takes 6 years of practice and a lot of documenting before sitting for boards. It's not specifically "zoo," but it'd help you stand out from peers without any certification.
ABVP – American Board of Veterinary Practitioners
Rumor has it though that that option is likely disappearing, but just rumor mill through the halls.
Definitely recommend sitting down with a boarded zoo vet and picking their brain. Or if you can find a resident, even better. Back to priority #1 though: get into vet school and finish that first. Maybe your interests will completely change during vet school - it happens all the time.
Good luck!