Lens and Camera Problem

I bought a 2nd hand sigma 17-50 lens from someone for my nikon d5300

However when I tried the lens on the camera there was just one problem.

When the lens is set to auto-focus, the display of the camera would focus rapidly between af-s and m. And also when i half press the shutter, the beep noise from focusing doesn't happen.

The manual mode of the camera works fine.

The internal focus is also not broken as the lens managed to auto focus for 5 seconds until it went back to the problem.

How would i go on about fixing this issue?

The first thing I would do is to clean the contacts; on both the camera and the lens. And also the glass on the lens, front and back.

Next I would borrow a Nikon camera and see if it focused. If not, try getting your money back. Next is to consider if it is worth it to have the lens repaired (probably not, but should be considered).

Neither your camera or lens have an auto focus motor.

The D5000 series needs a motorised lens for auto focus to work. Your lens is for a D7000 series which has a motor in the camera body.

If your body autofocuses with other lenses then it sounds as though you bought a lemon!
This is reinforced by the display flicking from af to m.

Bought online?

That's why I always advise to finish it with a meetup. Test thoroughly before paying.

I've had sellers bold enough to show up even with a clearly damaged lens or camera only to say they know nothing about it and end up praising me for being a pro. How much more for online deals?