How big would a disc have to be to blot out the sun covering 5% of the land mass of earth? Like this, but floating in space.



I imagine that this would also be influenced by the distance of the object from the sun, and that there is some ideal distance for this object to be? (and obviously the distance of the Earth from the Sun as well)
The angular diameter of the sun is approximately 30 arcminutes (roughly .0087 radians), or half of a degree.

The formula for angular diameter of a round object in radians is: 
$$
\delta = 2arctang\frac{diameter}{(2)distance}
$$

Given this, we should also think about position. Assuming we want to continually block the same spot on Earth we need to the orbital period to one year. (I'm not sure if there is a technical difference between orbiting the Earth once per year such that you're always between the Sun and Earth, and just plain orbiting the Sun)

According to this calculator, our sun blocker would need at a height of 2,152,050km to orbit Earth once per year. So, given that we can set up our formula with...

$$
.0087 = 2arctang\frac{diameter}{(2)2152050}
$$

...and the needed diameter of an object should come out to be about 18,722km in diameter. Given that, Mr. Burns's terrestrial solution is far more practical, though certainly a nice orbital one is far more devious. Being evil isn't cheap.

Edit:

This answer is a bit rough as it doesn't calculate for the 5% of the Earth's land mass stipulation. The answer which would meet this would depend on whether only an umbral shadow qualifies, or if a penumbral shadow would also suffice. I suspect probably the prior. The shadow would certainly reach the Earth, but probably not cover 5% of it, which is a shame considering its diameter is actually larger than Earth's. Regardless, it's not a very elegant solution.