I just got a Nikon D5200 how low should the F-stop be able to go?

Mine will only go as low as 4.5 and its in Manual mode, it there any setting that could be preventing it from going lower?

Lower?

The f/number may be lower, but the aperture is actually larger.

If your lens has a maximum aperture or f/4.5, then that is as wide an aperture you can have with that lens. If you want a lens with a wider aperture, you will have to buy a lens with a lens aperture of f/1.4, f/1.8 or f/2.8

If you are confused by the f/numbers here is how all that works

The "f" stand for fraction. An f/stop is the fraction of the length of the lens divided by the lens aperture

A 50 mm lens with a 25 mm aperture is said to be an f/2. Lens… 50/25=2 As the aperture gets smaller, the faction become smaller as well, like as in f/16 or f/22. Think of it as a fraction 1/2, 1/16 and 1/22

It depends on what lens you have mounted.

If you have the kit lens, that's 18-55mm f3.5-5.6.

What that means is that at 18mm the widest aperture is f3.5. At 55mm the widest aperture is f5.6. So it depends on how far the lens is zoomed out.

Remember the smaller the f number the widertthe lens aperture is.

If you want wider than f3.5 then you need to buy a faster lens eg 50mm f1.8.

The setting that prevents it going lower is the maximum aperture of the lens you have mounted.
If it is a zoom lens it will have a notation like - 18-55mm f/3.5-5.6
That means that at 18mm focal length you can set a max aperture of f/3.5; at 55mm the max aperture is f/5.6.
At focal lengths in between you will get f stops intermediate between f/3.5 and f/5.6

If you want wider then you need to buy a new lens - eg a 50mm f/1.4 allow a max aperture of f/1.4. - around 3-4 stops faster than the above zoom

I'm guessing f/3.5 at 18mm and f/5.6 when at 55mm. The lower the f/number, the larger the aperture size (or hole).

It has nothing to do with the camera body!
The f stop is a feature of the LENS. Check which lens you are using and waht the f range is.
You can buy lenses with a "faster" (wider f stop) but they can be expensive.

Since you just got the D5200, I would highly encourage you to take it back and get the D5200 body only and buy a separate lens with a larger maximum f/stop.
Here are the zoom lenses that have an aperture of f/2.8 or better - http://www.bhphotovideo.com/...rtclk=sort

If a different zoom lens isn't within your budget, then get the 50mm f/1.8 lens instead. It's sharp and cheap, a very rare combination found in lenses.