If you want to use WebAPI inside an existing MVC (5) project you have to do the following steps:
1.Add WebApi packages:
Microsoft.AspNet.WebApi
Microsoft.AspNet.WebApi.Client
Microsoft.AspNet.WebApi.Core
Microsoft.AspNet.WebApi.WebHost
Newtonsoft.Json
2.Add WebApiConfig.cs file to App_Start folder:
using System.Web.Http;
namespace WebApiTest
{
    public static class WebApiConfig
    {
        public static void Register(HttpConfiguration config)
        {
            // Web API configuration and services
            // Web API routes
            config.MapHttpAttributeRoutes();
            config.Routes.MapHttpRoute(
                name: "DefaultApi",
                routeTemplate: "api/{controller}/{id}",
                defaults: new { id = RouteParameter.Optional }
            );
        }
    }
}
3.Add the following line to Glabal.asax:
GlobalConfiguration.Configure(WebApiConfig.Register);
Important note: you have to add above line exactly after AreaRegistration.RegisterAllAreas();
protected void Application_Start()
{
    AreaRegistration.RegisterAllAreas();
    //\\
    GlobalConfiguration.Configure(WebApiConfig.Register);
    //\\
    FilterConfig.RegisterGlobalFilters(GlobalFilters.Filters);
    RouteConfig.RegisterRoutes(RouteTable.Routes);
    BundleConfig.RegisterBundles(BundleTable.Bundles);
}