The safer option would be to change the group of the storage directories to your web servers group (usually apache or www-data, but this can vary between the different operating systems) and keep the permissions as of the directory as 775.
chgrp -R www-data app/storage
Or with chown.
chown -R :www-data app/storage
Then make sure directory permissions are 775.
chmod -R 775 app/storage
From the Laravel web site:
Laravel may require one set of permissions to be configured: folders
within app/storage require write access by the web server.