Where can I find a NuGet package for upgrading to System.Web.Http v5.0.0.0?

You need the Microsoft.AspNet.WebApi.Core package.

You can see it in the .csproj file:

<Reference Include="System.Web.Http, Version=5.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35, processorArchitecture=MSIL">
  <SpecificVersion>False</SpecificVersion>
  <HintPath>..\packages\Microsoft.AspNet.WebApi.Core.5.0.0\lib\net45\System.Web.Http.dll</HintPath>
</Reference>