Typically I use following images for .net core 3.1 and it works fine.
FROM mcr.microsoft.com/dotnet/core/aspnet:3.1-buster-slim AS base
FROM mcr.microsoft.com/dotnet/core/sdk:3.1-buster AS build
I have for experimental reason started a new .net 5 project and created dockerfile with following
FROM mcr.microsoft.com/dotnet/core/aspnet:5.0-buster-slim AS base 
FROM mcr.microsoft.com/dotnet/core/sdk:5.0-buster AS build
and have following issue:
 => ERROR [internal] load metadata for mcr.microsoft.com/dotnet/core/sdk:5.0-buster                           0.2s
 => ERROR [internal] load metadata for mcr.microsoft.com/dotnet/core/aspnet:5.0-buster-slim                   0.2s
 => CANCELED [build 1/7] FROM mcr.microsoft.com/dotnet/core/sdk:5.0-buster                                    0.0s
 => => resolve mcr.microsoft.com/dotnet/core/sdk:5.0-buster                                                   0.0s
 => [internal] load build context                                                                             0.0s
 => ERROR [base 1/2] FROM mcr.microsoft.com/dotnet/core/aspnet:5.0-buster-slim                                0.0s
 => => resolve mcr.microsoft.com/dotnet/core/aspnet:5.0-buster-slim
 
     
    
