Stay on 5.6. Only use mysqli connections on new sites and pages you work on.
Update sites when you have time (mysqli will work on previous versions and can co-exist with mysql connections on the same site or even same page)
When you eventually upgrade to php7 all MySQL code will have to be upgraded to MySQLi. The shopping cart is not an issue it is all of the inserts and updates and recordsets. The database connection is what has drastically changed.