We would all prefer to forget the U.S. housing market crash. Six years later, it has grown more distant as the market continues to recover from record foreclosures and spiraling home prices. In October, permits for future home construction rose to their highest rate in nearly five-and-a-half years; home prices nationwide rose 12.5% in October from a year earlier (by comparison, they grew by 6% in 2012). Some markets have recovered more than others, though. Here's a look at the five strongest recoveries of 2013, thanks to data from Trulia, Zillow, and other housing experts.