Nginx and Docker with static html: Proxy pass does not forward to expected route

I want to serve static html as a service with Docker and nginx as a reverse proxy (there are also a python backend and mysql container, which I excluded here)

I have got the following docker-compose file:

version: "3.7"

  frontend:
    build: ./frontend
    container_name: frontend
    restart: always
    ports:
      - "5000:80"

  nginx:
    build: ./nginx
    container_name: nginx
    restart: always
    ports:
      - "80:80"

Dockerfile for Frontend:

FROM nginx:alpine
COPY . /usr/share/nginx/html

nginx.conf in my I do this:

server {

    listen 80;

    location /frontend {
        proxy_pass  http://frontend:5000/;
        #proxy_pass  http://frontend:5000; -> also tried this  
    }

}

Everything builds fine, but the proxy_pass does not work as expected.

Where I can reach my app:

http://localhost:5000/

Desired:

http://localhost/frontend

Error when I try to reach the latter route:

 /frontend/ HTTP/1.1", upstream: "http://172.27.0.2:3000/frontend/", host: "localhost"
nginx       | 172.27.0.1 - - [27/Jan/2022:19:11:07 +0000] "GET /frontend/ HTTP/1.1" 502 559 "-" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/97.0.4692.99 Safari/537.36" "-"

What did I do wrong?