When I try to run a2enmod php7.0 - I got message "Considering conflict php5 for php7.0".

After restarting apache - apache can't start.

How to solve this?

Maybe some already enabled modules links to php5?

Params: Ubuntu Wily, Apache 2.4.18, PHP 7.0.4 (works only cli)

First, disable the php5 module:

a2dismod php5

then, enable the php7 module:

a2enmod php7.0

Next, reload/restart the Apache service:

service apache2 restart

Update 2018-09-04

wrt the comment, you need to specify exact installed php-7.x version.