This 5.7" size popped up in a few rumors lately.
What nobody has noticed is that if you take an iPad mini screen (retina) and cut it in half you get a 5.7" display for a presumed Apple phablet, with a resolution of 1536x1024 and the same DPI as the iPhone 4-5.
Having devs optimize apps for 1536x1024 screen using iOS 7 auto-layout APIs, would pave the way for split-screen multitasking on iPads, which would be able to run two phablet apps side by side.
Using the same reasoning, Apple could also make a 4.3-4.5" iPhone with a resolution of 1024x768 and a DPI in between the iPhone and the 9.7" iPad.
An iPad could run four 1024x768 apps at the same time, and the 5.7" phablet could run two.