I just had the same problem and found your question while searching for a solution.
I got it working. The problem, for me, was that I initially targeted the .NET 4.0 framework when I added the EF 5 via NuGet. Changing the target framework and then reinstalling EF 5 via NuGet, fixed it. It's also possible (see comments) that just reinstalling EF 5 via NuGet is the solution for you.
I had the following line in the App.config file, notice Version=4.4.0.0:
<configuration>
<configSections>
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=4.4.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
</configSections>
</configuration>
So what I did was set the target framework to 4.5 inside the solution configuration and set the supported runtime to 4.5 too (inside the app config).
Old:
<startup>
<supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
</startup>
New:
<startup>
<supportedRuntime version="v4.5" sku=".NETFramework,Version=v4.5" />
</startup>
After that change, I removed EF 5.0 via NuGet and added it again. It gave me the following configSection as result, notice Version=5.0.0.0:
<configuration>
<configSections>
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=5.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
</configSections>
</configuration>
After that change, it worked.
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