Install the Backend Components

sudo add-apt-repository ppa:ondrej/php
sudo apt-get update
sudo apt-get install nginx git php7.3-fpm php7.3-mysql php7.3-mcrypt

Modify the PHP Configuration

sudo nano /etc/php/7.3/fpm/php.ini

Mudar a linha que tem:

;cgi.fix_pathinfo=1

para

cgi.fix_pathinfo=0

sudo service php7.3-fpm restart

Configure Nginx and the Web Root

sudo mkdir -p /var/www/laravel

sudo nano /etc/nginx/sites-available/default

Deve ficar assim:

server {
    listen 80 default_server;
    listen [::]:80 default_server ipv6only=on;

    root /var/www/laravel/public;
    index index.php index.html index.htm;

    server_name server_domain_or_IP;

    location / {
        try_files $uri $uri/ /index.php?$query_string;
    }

    location ~ \.php$ {
        try_files $uri /index.php =404;
        fastcgi_split_path_info ^(.+\.php)(/.+)$;
        fastcgi_pass unix:/var/run/php5-fpm.sock;
        fastcgi_index index.php;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        include fastcgi_params;
    }
}

Depois sai do arquivo e executa:

sudo service nginx restart

Install Composer and Laravel

cd ~
curl -sS https://getcomposer.org/installer | php

sudo mv composer.phar /usr/local/bin/composer

sudo composer create-project laravel/laravel /var/www/laravel

sudo composer create-project laravel/laravel /var/www/laravel 5.8

sudo chown -R :www-data /var/www/laravel

sudo chmod -R 775 /var/www/laravel/storage

Link de referência: https://www.digitalocean.com/community/tutorials/how-to-install-laravel-with-an-nginx-web-server-on-ubuntu-14-04