Inspiron 5150 laptops seem to have a lot of trouble with the inverter for the screen. As they begin to fail, you can sometimes have a variety of black and white video problems, partial gray screens, and such.
But it could be something as simple as a video graphics cable that has become loose, or a video graphics device driver that has gone bad.
Run the 8-steps to search out infestations that you will find elsewhere on this forum. If Ok, and your software appears normal, then you have work to do.
Assuming your software is oK, I would first download the driver for your service tag from the Dell support site. Once you know where it is located on your computer after download, go to the Device Manager (Start->Control Panel->System->Hardware->Device manager) and remove or disable the old driver, then install the downloaded version.
If no change, remove your keyboard. Remove the battery and power cord. Then, this may require removing six or eight screws from the bottom of the laptop, and changing some sliders slightly hidden in among the keys. Once the keyboard is loose, carefully with gloved hands, remove the very thin ribbon cable, then re-connect it.
Reassemble everything.
Now, if the problem persists, you should consider the inverter. It is about the size of a fountain pen, and rests at the bottom of the screen. You can buy the inverter on eBay. New. Do not get a used one, and get the exact model for your Inspiron 5150. Only a few are interchangeable..
The tricky part is that many of the screws to the screen are hidden behind rubberized screw covers, and they can be damaged during removal, resulting in an ugly look when reassembled. You can usually find replacement screw covers on eBay.
Otherwise, there is no difficulty. This is not rocket science, but it will take perhaps an hour or two. Remove all the screws that hold the screen assembly. Be careful to note which screws go where, as there are as many as four or five different screws and can be as many as 18 to 24 altogether. The inverter is at the bottom held on by screw clamps and simply unplugs like a two or three-prong lightbulb.
Plug in the new inverter. Replace the screws. Presto. Working again.