Hello,
MySQL server version 5.7 - it is latest stable version ( https:// dev.mysql.com/downloads/mysql/ ).
Client API library version => mysqlnd 5.0.11-dev - it is rigth version for PHP 5.6
Finally, i can't install Blesta 4.0 as new install, but successfully install Blesta 3.6 and the upgrade this to Blesta 4.0.
Additionally, i don't use Apache and have nginx+php-fpm.
For reproduce this, if you want, i can setup a new VPS for you and then setup identical OS and software (Ubuntu 16 + VestaCP + PHP 5.6 + nginx) and provide you root access. Please, inform me if this need.