NET core рекомендуют  размещать за реверс прокси. 
Так что читаем  официальную инструкцию
https://docs.microsoft.com/ru-ru/aspnet/core/host-...
<br>
server {<br>
    listen        80;<br>
    server_name   example.com *.example.com;<br>
    location / {  # main location<br>
        proxy_pass         http://localhost:5000;<br>
        proxy_http_version 1.1;<br>
        proxy_set_header   Upgrade $http_upgrade;<br>
        proxy_set_header   Connection keep-alive;<br>
        proxy_set_header   Host $host;<br>
        proxy_cache_bypass $http_upgrade;<br>
        proxy_set_header   X-Forwarded-For $proxy_add_x_forwarded_for;<br>
        proxy_set_header   X-Forwarded-Proto $scheme;<br>
    }<br>
    location /blog/ {<br>
        proxy_pass         http://localhost:5001;<br>
        proxy_http_version 1.1;<br>
        proxy_set_header   Upgrade $http_upgrade;<br>
        proxy_set_header   Connection keep-alive;<br>
        proxy_set_header   Host $host;<br>
        proxy_cache_bypass $http_upgrade;<br>
        proxy_set_header   X-Forwarded-For $proxy_add_x_forwarded_for;<br>
        proxy_set_header   X-Forwarded-Proto $scheme;<br>
    }<br>
}<br>