Hi,
The LCD screen flex cable connection to the motherboard may be loose or the LCD screen may have failed. Either way the tablet needs to be opened to ascertain the problem.
Here is a link to the [[Topic:Samsung Galaxy Tab 3 10.1|ifixit guide(s) Samsung Galaxy GT-P5200]] to repair your tablet. They are useful in that they show how to disassemble the tablet to gain access to the LCD screen and its' connection to the motherboard.
Here is a [https://www.etradesupply.com/catalogsearch/result/?warehouse=0&q=galaxy+p5200|link] to a supplier of the parts for your tablet. It is not a recommendation to use them, it is shown to give an idea of the cost of the part. There are other suppliers that may suit you better. Just search online.
Hopefully this is of some help.