The permissions for the storage and vendor folders should stay at 775, for obvious security reasons.
However, both your computer and your server Apache need to be able to write in these folders. Ex: when you run commands like php artisan, your computer needs to write in the logs file in storage.
All you need to do is to give ownership of the folders to Apache :
sudo chown -R www-data:www-data /path/to/your/project/vendor
sudo chown -R www-data:www-data /path/to/your/project/storage
Then you need to add your computer (referenced by it's username) to the group to which the server Apache belongs. Like so :
sudo usermod -a -G www-data userName
NOTE: Most frequently, groupName is www-data but in your case, replace it with _www