Nikon D5300 camera - multiple shots?

I just got a Nikon D5300, but I think there's something wrong with it.
I set the camera settings to both Continuous H and Continuous L but it only takes a single frame.
Am I doing something wrong? Do I have to change something else?

I know it's a stupid question but I would appreciate the answer

You need to keep your finger pressed down on the shutter release.

LOL… Same as BK, my first thought was to ask if you know you have to keep holding the shutter button down. You don't just push and release the button and the camera starts taking photos continuously by itself. It will take photos only as long as you hold down the button.

You already have two good answers from "Steve P. And BK. I would suggest you approach these questions like I do while reading the manual ( I have read my manual 3 times), by keeping the camera in hand and firing off shots to practice using what you have just read. If you had done this, you would naturally hold that shutter release longer at some point and realized on your own that holding down the shutter release results in repeated shots. So what if the camera fires multiply times. However it stands to reason that you have or had tranferred any shots you want to keep to your computer and the back-up drive that we all recommend. The card you are using for this learning exercise can them be reformatted as a "learning tool" and can be reformatted, when you are ready to put the memory card into pictures you want to keep service.

In Continuous H mode, it's take about 5 photos per second -- while you hold the shutter button down

Continuous L mode takes about 3 photos per second -- while you hold the shutter button down.

Format the card. If that does not do the trick, use a faster card with of at least Class 6.

Are you holding the button down? You should be pressing down continuously for the camera to shoot in rapid succession. It only stops wither when you lift your finger or when the buffer is full. It's a camcorder so temper your expectations. Continuous mode doesn't last very long with digital cameras.