Because EEPC5.2.1 was EOL when 7.1 was released, it was not tested for upgrade, thus the lack of official support.
it may work, it may not - it's unknown. You can test it yourself, or if you want to follow supported processes only, you'll need to either upgrade 5.2.1 to 5.2.13 and then go to 7.1, or go 5.2.1>7.0 and then 7.0> 7.1
Regardless though, 5.2.1 is EOL since March 2014 so you won't be able to get any support for the upgrade - my advice therefore would be to do your own validation of a 5.2.1>7.1 upgrade to save on that intermediate step first. If it works it will save you a lot of effort.