2 possibilities. First, dirty video cable contacts. Remove the battery & power supply. Then  remove the screen bezel & keyboard in order to re-seat the video ribbon cable connections a half dozen or so times to clean the contacts.

Second, if you have a habit of opening/closing the lid a lot, the ribbon cable itself might've developed a conductor break usually near the congested hinge area. Replacments are fairly inexpensive.

http://www.amazon.com/LotFancy-Notebook-Compatible-numbers-50-4CG13-022/dp/B00637VC4C/ref=sr_1_1?s=pc&ie=UTF8&qid=1425909641&sr=1-1&keywords=aspire+5738+video+cable

Jack E/NJ 

Not too hard. There are likely two small phillips head screws hidden behind round tape covers at the bottom of the screen bezel. Once they're out, the bezel should lift up. The screen ribbon connectors may have a piece of gummy tape securing it. Remove the tape, and reseat several times. Either re-use the tape or scotch tape it to secure.

The motherboard connector end of the ribbon requires removing the keyboard, which isn't as easy unless you have 3 pairs of hands. It's usually held in place by a half dozen plastic catches near the top edges & sides of the keyboard. They're prone to breaking but aren't a big deal since the keyboard can be easily held in place with designer-color duct or electrician tape that won't be noticed. My keyboard and case are black so plain old electrician tape does the job.

I'd try removing the screen connector first. And see if that works out for you. Don't forget to remove the battery while you're trying to reseat these connectors.

Jack E/NJ