Storing files outside the Laravel 5 Root Folder

The laravel documentation could give you a helping hand.

Otherwise you could go to config/filesystems.php and add your own custom storage path for both local and production:

return [

    'default' => 'custom',
    'cloud' => 's3',
    'disks' => [

        'local' => [
            'driver' => 'local',
            'root'   => storage_path().'/app',
        ],

        'custom' => [
            'driver' => 'custom',
            'root'   => '../path/to/your/new/storage/folder',
        ],

        's3' => [
            'driver' => 's3',
            'key'    => 'your-key',
            'secret' => 'your-secret',
            'region' => 'your-region',
            'bucket' => 'your-bucket',
        ],

        'rackspace' => [
            'driver'    => 'rackspace',
            'username'  => 'your-username',
            'key'       => 'your-key',
            'container' => 'your-container',
            'endpoint'  => 'https://identity.api.rackspacecloud.com/v2.0/',
            'region'    => 'IAD',
        ],

    ],
];