Can I use Linq to SQL in asp.net 5 mvc 6?
There is no "Linq to SQL Classes" in "Add New Item" form

I know its not supported in dot net core 5 but I don't need dnx core 5 and cross platform feature. I'm ok with dnx core 4.5.1
How can I add Linq to SQL Classes file (.dbml) to MVC 6 Project?

LINQ to SQLhas been depricated ages ago. You will need to look into using Entity Framework going forwards, if you want to use a Microsoft supported ORM. Is LINQ to SQL deprecated?