As WHMCS 7 was not written to support modern MySQL syntax, you must make customizations to MySQL to install and use WHMCS 7 with MySQL 5.7.
SSH in to your server as root and create a new configuration file using nano or the editor of your choice:
sudo nano /etc/mysql/conf.d/disable_strict_mode.cnf
In the file, enter these two lines:
[mysqld] sql_mode=NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
Finally, restart MySQL with this command:
sudo service mysql restart