Yes, 5D has bracketing... it would be fairly obvious if it's taking three shots though. Is mirror lockup enabled? I think there's a setting that keeps it from cancelling after a single exposure. Or have you accidentally set the 2 second self-timer, which flips the mirror up for a short time before taking the shot? Or accidentally set the camera to B, which flips the mirror up and opens the shutter as long as you keep pressure on the shutter release button?
Another possibility... not sure if it's the same on 5D as my 5DII, but Long Exposure Noise Reduction, if it's set, causes long exposures to take twice as long. This is because after the initial exposure the camera takes a second image of equal time, with the shutter closed, to compare and identify noise for removal. I rarely use this and frankly haven't looked to see if the mirror remains up during this process. But if it does it's another setting that might give the impression the mirror is sticking in the up position for a short time.
As Eagle noted, this shouldn't have anything at all to do with the lens. The 50/1.8 is fully compatible with the camera (actually it's compatible with all EOS cameras ever made... film or digital). However, look at the rear of the lens for any odd protrusions that might get in the way of the mirror.
You should be able to fire the 5D without any lens on it, to see if the mirror still sticks.
The most common fault that causes the mirror to hang up is failing light seals. The seals are open cell foam, and also act as sort of a bumper for the mirror. Sometimes they get sticky and gummy, from old age and possibly exposure to heat. With the mirror down, look for any black particles or smears around the outer edges of the mirror, which would be a sign the seals need replacement. Alternatively, you might very carefully touch the foam seal with a finger tip to see if it feels sticky... just don't touch the mirror! Seal replacements should be done professionally. Doesn't have to be sent to Canon, a good local camera repair shop should be able to handle it. It's not an uncommon, difficult or expensive job... but requires some care to avoid damaging other things in the camera.
Another thing, it's a common problem on 5D classic for the mirror to come loose from it's mount. Originally it was merely glued in place. If it's slightly askew, it could hang up on other things in the mirror box. Usually it comes completely loose and is flopping around inside the camera. But, who knows! Maybe it just slipped a bit in your camera. Canon will repair this situation for free.
A couple other things... I don't have a 5D here to check, but on many Canon there's a metal baffle right inside the lens mount, that the mirror closes close behind. If that's bent, it might drag on and cause the mirror to stick.
One other thing, the camera has an interchangeable focus screen. Check to see that the frame holding it in place is fully closed and latched. Usually it would flop completely open letting the focus screen drop out of place, but who knows! Maybe it's partly open or the metal frame is bent, catching the mirror and causing it to stick.