无法从浏览器访问Docker应用程序

我有一个.NET Core 2.1 API，当通过Windows中的Visual Studio运行时，它会从浏览器接收HTTP GET，并成功地从MySQL数据库返回数据。

我一直在尝试将API添加到Docker容器（在Ubuntu内）-可以构建，但是我无法从浏览器访问API：

我已经试过：

• 检查可用端口。这是相关的输出：

• 使用其他浏览器进行连接：在Chromium中，它显示“无法访问此站点：本地主机意外关闭了连接。”
• Testing unused ports in the browser to see if this returns a different message - for Firefox, unused ports return 'Unable to connect' instead of 'Secure connection Failed', and in Chromium they return 'localhost refused to connect.' instead of 'localhost unexpectedly closed the connection.'
• In Firefox, configuring 'security.tls.insecure_fallback_hosts' to 'localhost'.
• Double-checking that ports are mapped correctly in docker-compose.yml - under 'ports' for the relevant container, 44329 is mapped to 44329.
• Running a DB query when the API starts and logging the result: this is successful. I run docker-compose up, the API starts, connects to the DB container, and it logs the result of an SQL query to a text file. So the problem is unlikely to be anything to do with the database.
• Logging GET requests: Inside Windows, the GET requests are successfully logged, but in the Ubuntu Docker container, they're not.

This might be relevant: In Windows, the API only works properly if you start it from Visual Studio. If you execute dotnet webapi.dll, you get this output

...\netcoreapp2.1>dotnet webapi.dll
...
Now listening on: http://localhost:5000
Now listening on: https://localhost:5001
Application started. Press Ctrl+C to shut down.

So here it's not running on 44329; instead it's accessible via 5001 in the browser, where you get this message which is not chill at all: Clicking 'ADVANCED' allows you to continue to the API.

• So I've also tried connecting via 5001 in Ubuntu without luck.

Here's the output from 'docker-compose up':

matt@Matt-Ubuntu:~/docker2$ docker-compose up
Starting docker2_mysql_1 ... done
Starting docker2_dbmodelmapper_1 ... done
Attaching to docker2_mysql_1, docker2_dbmodelmapper_1
... (mysql stuff) ...
dbmodelmapper_1  | Hosting environment: Production
dbmodelmapper_1  | Content root path: /app
dbmodelmapper_1  | Now listening on: http://[::]:80
dbmodelmapper_1  | Application started. Press Ctrl+C to shut down.

• Seeing the port 80, I've tried connecting to that, without success.

• The relevant container as shown by docker ps is:

  

What kind of issue am I looking at here?