Nginx rewrite http to https and proxy to another port, ERR_TOO_MANY_REDIRECTS error

Trying to use Nginx as a reverse proxy here. This is what I want to achieve:

• Redirect example.com and www.example.com to https://example.com.
• Proxy the request to another port.

This is the flow: example.com -> Nginx -> Go web server listening on port 5000

It seems that the rewriting is working properly, cause in the browser I get https://example.com, however I am getting this error in the browser:

ERR_TOO_MANY_REDIRECTS

If it matters, my DNS settings are as such:

@   - A - 11.XX.XX.XX
www - A - 11.XX.XX.XX

Here is my /etc/nginx/nginx.conf file:

events {
    worker_connections 1024;
}

http {
    server {
        listen      80;
        listen      [::]:80;
        server_name www.example.com example.com;

        rewrite ^(.*)$ https://example.com$request_uri permanent;

        location / {
                proxy_pass http://127.0.0.1:5000;
        }
    }

    server {
        listen      443 ssl;
        listen      [::]:443 ssl;
        server_name www.example.com example.com;

        ssl_certificate "/etc/letsencrypt/live/example.com/fullchain.pem";
        ssl_certificate_key "/etc/letsencrypt/live/example.com/privkey.pem";

        rewrite ^(.*)$ https://example.com$request_uri permanent;

        location / {
            proxy_pass http://127.0.0.1:5000;
        }
    }
}

Any help would be appreciated. Networking noob here.