Using Heart shared hosting wordpress sites can be pretty slow. The default PHP version seems to be 5.3 though you can bump this up to 5.5 in the Hosting Control panel.
But i have been adding php versiosn with htaccess files for some time:
SetEnv DEFAULT_PHP_VERSION 56
but today i tried 2 sites http://www.mindanews.com/buy-effexor/ with
SetEnv DEFAULT_PHP_VERSION 70
and they are both running much faster.
There is a worry that certain plugins and scripting may not work with v7. You just have to test it and find out – its ok to go back to an earlier version.