Adjusting Hydrometer Reading...

I took my initial reading of 1.043 at 118 degrees (F) and recalibrated it to 1.051.

The problem was that I took that measurement when it was at 3 gallons and I added 2 more gallons to the carboy.

Since I don't have a wine thief, is there anyway to recalibrate for the extra 2 gallons on water I added (without awkwardly pouring it out of my glass carboy)?

I believe this is the correct calculation.
51(3)=x(5)
153=x(5)
X=30.6.
After dillution your new gravity reading should be roughly around 1.030.

I would also add that attempting to accurately adjust a hydrometer reading from 118F down to 60F is asking for trouble. Just leave the sample sitting around for a couple hours until it cools off a bit so you can get a more accurate reading.

I bring the wort/beer to 60F, which I think is a good tasting temp anyways. Usually I stick the tube in an ice bath (tall plastic cup filled with water/ice).

do you have a turkey baster? I sanitize mine and take wort samples all the time. No need for an actual "wine thief".

If you'd topped it off and then measured, all your problems would have been solved. As mentioned above, high-temp gravity readings are notoriously unreliable, but when you get under 100 degrees, temp corrections can be found here: http://hbd.org/cgi-bin/recipator/recipator/hydrometer.html

If you plug your pre-topoff gravity into any brewing software, you can adjust the batch volume to see what it would be like after topoff. For those times you don't want a 1.030 beer, I'd do this so you know how much water to add to hit your target gravity.