Could not load file or assembly ‘System.Web.Http, Version=5.0.0.0

I had the same error while deploying previously converted (from .NET 4.5 to 4.0) web app on IIS 6.0.

In the web.config runtime section I've found

<dependentAssembly>
    <assemblyIdentity name="System.Net.Http" publicKeyToken="b03f5f7f11d50a3a" culture="neutral"/>
    <bindingRedirect oldVersion="0.0.0.0-4.0.0.0" newVersion="4.0.0.0"/>
</dependentAssembly>

which I've changed to

<dependentAssembly>
    <assemblyIdentity name="System.Net.Http" publicKeyToken="b03f5f7f11d50a3a" culture="neutral"/>
    <bindingRedirect oldVersion="0.0.0.0-1.0.0.0" newVersion="2.0.0.0"/>
</dependentAssembly>

Now works like charm.

Visual Studio 2013 has a new feature to take care of this. When you build the app, you should see warnings about different versions of an assembly being referenced. Double click the warning to add assembly binding redirects to the web.config.

See http://msdn.microsoft.com/en-us/library/2fc472t2.aspx for more details.

jeff.eynon notes below that you need to have the web.config checked out (if using TFS source control) to get VS to edit the file automatically. Thanks for the tip!