Well, that's going to be tricky. You'll probably get various pieces of advice in here regarding ways to "fake it," matting and inserting your screen in post. But I'm assuming that you want to and/or for some reason have to do it practically and really shoot a real screen.
Of course the "right" way to do this is to shoot with a camera with a "clearscan" mode, where you dial in an exact shutter speed to perfectly sync with the TV scanning. Unfortunately this is one of those cases where videographers who use DSLRs have to admit that they are using a tool that is primarily a still camera that just incidentally can shoot video. Ergo, the 5D, being a still camera, does not have a clearscan mode.
The first thing to do will be just to play with your shutter speed (that's shutter speed, not frame rate). Heck, try it at a normal shutter speed in your first test... you might get lucky and have scanning minimal enough that it is acceptable. If/when it proves not, then start trying all the nearest adjacent shutter speeds. You might find one that looks good enough (which will probably be a slightly slower shutter speed). Don't veer off the norm too much, you'll want to stay as close as possible to a "normal" shutter speed that still works ("normal" being one over twice the frame rate).
If that doesn't work and you don't have any people/animals/machinery in the shot that would give away incorrect motion speed, there is something else you can try. You can produce special content for playback on the TV that runs slower than normal speed. Content running at 50% speed would be a good start, although 25% might work even better. When you shoot this, you can set your shutter speed quite slow and eliminate the lines. Then in post you speed the footage back up by the appropriate amount to get back to "normal" speed. With the right combination you can eliminate the scan lines, though it may bear a fair little bit of testing. Again, you just can't (easily) have anything in the scene (such as a moving person) that would give away that you're viewing a non-normal-speed shot.
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