I have an existing site in Sitecore 7.2. I would like to move the site out of Sitecore and into a new MVC 5 project. I would like my users to be able to use their existing credentials. It seems to me, from the database scheme, that Sitecore is using SQL Membership to manage the user store. I have run aspnet_regsql.exe to setup a new database and it has the same structure as the Sitecore database.
I have added the following to my new web.config.
<profile defaultProvider="DefaultProfileProvider">
<providers>
<add name="DefaultProfileProvider" type="System.Web.Profile.SqlProfileProvider, System.Web.Providers, Version=2.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</profile>
<membership defaultProvider="DefaultMembershipProvider">
<providers>
<clear />
<add name="DefaultMembershipProvider" type="System.Web.Security.SqlMembershipProvider, System.Web.Providers, Version=2.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" enablePasswordRetrieval="false" enablePasswordReset="true" requiresQuestionAndAnswer="true" requiresUniqueEmail="true" maxInvalidPasswordAttempts="5" minRequiredPasswordLength="6" minRequiredNonalphanumericCharacters="0" passwordAttemptWindow="10" applicationName="MyApplication" passwordFormat="Hashed" />
</providers>
</membership>
<roleManager defaultProvider="DefaultRoleProvider">
<providers>
<add name="DefaultRoleProvider" type="System.Web.Security.SqlRoleProvider, System.Web.Providers, Version=2.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</roleManager>
When I run my new test project it creates additional tables in my new database and is not using the ones that were created with aspnet_regsql.exe.
My question is, what do I need to add to my new MVC 5 web.config and elsewhere to force my new project to use the SQL Membership tables created with aspnet_regsql.exe?

It is possible to use the old membership with MVC5 but it is better to migrate to ASPNET Identity provider. Thus you do it once and will not face compatibilty problems in future. Here is a link: http://www.asp.net/identity/overview/migrations/migrating-an-existing-website-from-sql-membership-to-aspnet-identity