I have installed php 5.6 and and php 7.1 on my Ubuntu 16.04
I know with Apache as my web server, I can do
a2enmod php5.6 #to enable php5
a2enmod php7.1
I think you should try this
From php5.6 to php7.1
sudo a2dismod php5.6
sudo a2enmod php7.1
sudo service apache2 restart
sudo update-alternatives --set php /usr/bin/php7.1
sudo update-alternatives --set phar /usr/bin/phar7.1
sudo update-alternatives --set phar.phar /usr/bin/phar.phar7.1
From php7.1 to php5.6
sudo a2dismod php7.1
sudo a2enmod php5.6
sudo service apache2 restart
sudo update-alternatives --set php /usr/bin/php5.6
sudo update-alternatives --set phar /usr/bin/phar5.6
sudo update-alternatives --set phar.phar /usr/bin/phar.phar5.6