Grainy images of what look like a bigger iPhone's casing showed up today on Twitter from the same guy The images are really sketchy and believe what you want, but assuming this is the real deal, I did some back of the line, rough calculations and found the resulting screen size, surprisingly close to 4.7" diagonal! And by the way look how thin it is, looks almost half the size of the current iPhone, not sure what that means to the back camera? Apple probably could afford to thin the iPhone this much thinner, probably by making the backlights thinner and lighter, like this report from MacRumors suggests.
With these images, I was too tempted to do some rough calculations to come up with some numbers from these images. Now when you do not have the casing with you in hand, though it is impossible to measure the dimensions, you can calculate approximate dimensions using shapes that do not scale up or down, for example, I use the size of the Touch ID enable home button's diameter (for the longer side) and the lighting connector's width for the shorter side, as constants, like shown below and compared them to the measurements on my iPhone 5. Note that since the images here are taken at an angle, there is always an error associated with the calculations, I would say approximately 5% or less.
The ratio of the width of the lightning connection in my iPhone 5 is around 0.9cm/6cm and in this image it was around 9squares/60squares, so exactly the same! So to the first order this casing is the same width as the iPhone 5 and 5S. Now let us use the same technique for the longer side of the iPhone as well. The ratio of the diameter of the home button to the total length of the my iPhone 5 was 1.1cm/12.2cm or approximately 0.09 and for this casing it was 65squares/700squares or approximately 0.0928, i.e., 3% more, but I would say this difference is within my error limit. So in conclusion both the width and length (from the top view, while viewing the screen) of this casing is almost exactly the same as the iPhone 5.
But there is no doubt that this casing's screen looks bigger, how is that possible with the same external dimensions of the front panel? Like I have repeatedly said (as early as yesterday), the only other way to increase the screen size without increasing the overall iPhone dimensions, is by reducing the bezels on the sides. So using the same crazy calculations, let's calculate the bezel size of the this casing. My iPhone 5 has equal bezel width on the longer side of it of 1.6cm (near the home button) and 1.6cm (near the front facing camera and the hearing piece), so 3.2cm out of the total 12.2cm of the front panel is bezel. So actual screen size is approximately 73% of the panel. This casing however has thinner bezels, of 80squares near the home button and 45squares near the hearing piece on the top. And with the total height of the front panel being 700squares, the actual size of the touch screen is approximately 83%. So from 73% screen on the iPhone 5 it is now 83% on this casing. Assuming the side bezels did not change (this assumption is false as clearly from the above pictures, the side bezels are also thinner), this means that the diagonal size of this casing is 83/73 times the larger that current 4" (diagonal) on the iPhone 5. Or this casing is approximately 1.13 X 4" = 4.55" (actually a little more than 1.13 times, as when a side of a rectangle increases by x%, its diagonal increases by a percentage greater than x - Pythagoras theorem, for simplicity sake lets take it as 1.13 times). Now, more real estate can also be gained from trimming the side bezel, so let's say we gain another 0.2" (at least) and we come to a diagonal screen size of approximately 4.7! That is awfully close to one of the rumored [WSJ] bigger screen iPhones.
These are sketchy, grainy images and might not even be the real deal, but in the rare chance that they are, they add up to a 4.7" diagonal screen, with the exactly the same outer dimensions of the current iPhone 5 and 5S. This is indeed wonderful news (if true, of course) as this means, we can still use this bigger screen iPhone with one hand. So there you go, you can have your cake and eat it too! Now coming to the other bigger screen iPhone, the one with 5.5", I have no clue about that.