I used a Nikon D5300 for chase season 2014, which is almost the exact same thing as your D5200.
It's a great camera, and like most modern DSLR's, is very capable of recording fantastic storm shots - but a lot of this is up to the person behind the camera. It's important to know your camera inside and out, so you can switch modes / ISO / other settings quickly and not futz around scrolling through menus when you are in rapidly changing conditions. Experiment with different types of metering - I suggest you begin with matrix rather than center-weight or spot. You will find autofocus has problems against gray, non-contrasty skies, so get comfortable focusing manually and (like mentioned in other replies) don't forget composition, because taking 30 steps into a farm field in order to get some power lines out of the picture can make the difference between an "okay" picture and a spectacular one!
Practice shooting clouds NOW. Do you like what you capture? What can you do differently?
If you want your pics to show towering white storm towers contrasted against a dark blue sky, you need to use a circular polarizing filter (~$30) on your lens, but you should take it off before you get under the meso, where things get dark. Like others have suggested, you will rarely use a long lens when chasing. The Nikon 18-55 or 18-140 are good all-purpose starter lenses, but you will find yourself wishing you had a wider-angle lens any time the entire sky is filled with mammatus or a huge shelf cloud is a half-mile away and closing in. For DX cameras such as yours, the Tokina 11-16mm f/2.8 AT-X116 Pro DX (about $450) is a great choice for wide-angle work.
When you are under the meso in relatively dark conditions, you will probably want to use the largest aperture available with ISO set such that your shutter speed is fast enough to hand-hold without blur - 1/60 second being a common threshold. Resist the urge to zoom when hand-holding in low-light conditions because you will increase your chance of blurring the pic - getting a sharp pic is essential because then you can digitally zoom/crop later in post-processing** (<-- shoot in large/fine format so you can get the most of your available 24 megapixels)
**You will take a TON of pics on a chase, then get home and find your camera didn't record the scene like it appeared to your eyes. It's NOT the camera - we ALL deal with this, so get familiar with photoshop or similar editing utilities to help you recreate the contrast and pull out the colors so you can show others what YOU saw. It's not cheating - even the most expensive camera can't replicate the dynamic range and color complexities of the human eye.
I shot the pic below with my D5300 and the 18-140mm kit lens.
Best wishes,
TR