Default menu section in MVC5 template looking like that:
If I recall correctly you can specify the DisplayTemplate in the Menu() method.
Navigate to ~/Views/Shared/DisplayTemplates and create a new view called MyMenu.cshtml.
Set the model type to MvcSiteMapProvider.Web.Html.Models.MenuHelperModel and then specify the menu structure (with HTML).
MyMenu.cshtml
@model MvcSiteMapProvider.Web.Html.Models.MenuHelperModel
@using MvcSiteMapProvider.Web.Html.Models
Now change your Menu() method.
@Html.MvcSiteMap().Menu("MyMenu")