Is MySQL 5.7 compatible?
Yes. MySQL 5.7 is compatible with D7.x. Per the docs:


  Drupal 7 supports MySQL 5.0.15/MySQL 5.1.30/MariaDB 5.1.44/Percona
  Server 5.1.70 or higher, and requires the PDO database extension for
  PHP (see What is PDO?).


Is it safe? Maybe. It depends on your code/infrastructure setup. 

Just because a web application is compatible with a version of a DB server, doesn't mean an upgrade will happen flawlessly. There can be many things that could go wrong (e.g. hidden dependencies). 

It will probably be fine with a minor version upgrade, but always have a test/backup plan in place when rolling out infrastructure changes.