When upgrading Jira from these 6.x versions, we would recommend going to a 7.0.x version first. Once that upgrade is complete, be sure to update all the plugins you use with Jira at this version. Only then is it safe to then upgrade to the latest versions like 7.5.x.
Jira supported MySQL 5.1.x up to the Jira 7.1.x line. After that support for that database was dropped. You can find the corresponding Jira supported platforms info in that link.
I would recommend upgrading Jira to a 7.0.x first, then you can either migrating the database or upgrade the database to a 5.6.x version. Upgrade JIRA 7.2 - JIRA Knowledge Base - Atlassian Documentation also has a lot of good information in regards to upgrading these older versions of Jira to 7.2.x and higher and the very common pitfalls users find.
Regarding Confluence: technically the version you are running (5.7), does not support that version of that database per Confluence Supported Platforms 5.7.
The other thing about running these products on a MySQL platform is that Atlassian installations are not able to bundled updated JDBC drivers with these install packages. So it's a good idea to also update the JDBC driver at the time you do an upgrade or even before the upgrade. These tend to help with performance and reliability.
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