This topic must've been beaten to death on here, but still, I want to know how to overexpose an image background in Lightroom 5. Below are the two images for reference:

Try the Local Adjustment Brush tool. Turn on the Overlay Mask so you can see where your painting. Auto Mask may help control any spill on your subject. Adjust the Exposure and Highlight sliders to bring the background up to white. You may be able to use the Spot Removal tool to get rid of any lines from the background. Good luck.