I purchased a Tamron 70-300 mm lens for my Nikon d5300 a few days back. Its autofocus worked perfectly. But now it doesn't work at all.
I am a beginner and I don't know much about it. Why would it stop auto-focusing?
Depending on which Tamron lens you have there could be a switch on the left side of the lens itself to toggle between "AF" and "MF". Make sure it is still set to AF.
There are various ways to change the focus mode of the camera itself, but that can vary with the button configuration. You'll need to go through the manual and check the settings in the menus to learn how to identify what focus mode it is in, and the numerous ways you can (sometimes inadvertently) change that.
It seems like newer Tamrons have problems with the autofocus motor. My 70-200/f2.8 VC had the same symptoms and after a while it stopped focusing but was repaired through warranty. I hear similar stories about the new 24-70/f2.8 VC as well. First of all go back to your camera store and let them check it out and show you how it works. If there's a problem send it back for replacement or repair. You should not have to clean contacts on a new lens.
It seems that there is an issue with the Nikon D5300 and Tamron lenses, based on other forums, so when that happens you should check your display to see if says "no lens attached" or "no objective mounted." I have a similar problem with the Tamron 150-600mm and so far only disconnecting and reconnecting the lens seems to work. Sometimes I've had to do this 2-3 times before it starts working again.
I had the same problem with my 70mm-200mm f2.8 Tamron VC, where it stopped auto focusing and had it repaired through warranty. Not sure why this happen, I rarely use the lens, it's never be abused and still looks new. The repair report stated that the pc board, VC reset and a general cleaning. Works as expected now but not sure if and when it will stop working again.