During Apple's quarter earnings call, CEO Tim Cook took a question on whether or not Apple would consider shipping an iPhone with a 5-inch display. The question is pertinent not only because of sporadic rumors that Apple was considering a larger iPhone, but because so many of the iPhone's top-tier competitors have larger displays. Cook began as you'd expect, praising the current iPhone 5's screen, "iPhone 5 has the absolute best display in the industry," he said. Cook then began a small session about what sorts of "tradeoffs" go into a smartphone display, including "resolution, color quality, brightness, reflectivity, screen longevity, power consumption, portability, compatibility with apps, many things."
"We would not ship a larger display iPhone while these trade offs exist."
Although Cook didn't rule out the possibility, he said that Apple "would not ship a larger display iPhone while these trade offs exist." Presumably the biggest on on that list would be "compatibility with apps," as Apple just recently made developers create new versions of their apps for the iPhone 5 and would likely prefer not to do it again so quickly.
Cook also pointedly took a shot at other devices that ship with larger displays, saying "our competitors have made tradeoffs to ship a larger display." Surprisingly, he didn't mention one-handed use as one of those tradeoffs, instead implying that they fell short in the factors already mentioned. Although Cook may be right that many Android smartphones ship with disappointing screens, it's not as if the relatively worse color fidelity and white balance on the Samsung Galaxy S3 have stemmed its sales.
Cook's statements don't entirely preclude a larger iPhone in the future, but the hints do make it appear slightly less likely — that is, unless Apple would rather tout its ability to master those persnickety "tradeoffs."