Q:

asp.net 5 web api - right tool for the job? 

I have a number of tables inside a database that I use for 4-5 different websites.   These tables already exist and have plenty of data and views/stored procedures/functions etc.  already completed. 
I would like to provide an api to give access to each of these tables to whichever website I happen to be using so they're accessing the data in a consistent manner.   I have Visual Studio 2015 and have been trying to create a Web Api using EntityFramework. 
However, every tutorial I find for accessing databases insists on creating the database and tables within the code for the api, and utilizes just the tables with the various CRUD actions handled within.  
As I have the tables built, I don't want to recreate them, and as I have some programming already in place using functions/stored procs, I don't really want to reinvent the wheel and recreate it all. 
I did find this: http://www.c-sharpcorner.com/UploadFile/4b0136/working-with-stored-procedures-using-entity-framework-part/  for EF6 (though I believe I'm using EF7, but that seems to be importing each function in turn, which seems.. kludgy)
So my question is two-fold:

Is ASP.NET 5 web api the right tool for the job?  
Can the ASP.NET 5 web api handle stored procedures easily? 

A:

At time of writing it's currently easier to build an API over an existing database using ASP.NET 4.6 and EF 6.  This tutorial describes how you can go about building a model from an existing database:
http://www.asp.net/mvc/overview/getting-started/database-first-development/creating-the-web-application
Once you have a model and your classes in place, you can then follow any article on scaffolding Web API.