Operand type clash: my first User Defined Type with list of Integers, how to test via SSMS
As you have declared dbo.StringList to be a User-Defined Table Type, you have to utilise it as you would a table.

So instead of assigning '1,2,3,4,5' as a string, you must INSERT this value into the table.

There's a pretty decent example in BOL, but I'll create one based on your example above.

CREATE TYPE [dbo].[StringList] AS TABLE(
  [Item] [NVARCHAR](MAX) NULL
);

GO 
CREATE PROCEDURE [dbo].[sp_UseStringList]
    @list StringList READONLY
AS
BEGIN
    -- Just return the items we passed in
    SELECT l.Item FROM @list l;
END

GO


DECLARE @StringList StringList

INSERT Into @StringList values('1,2,3,4,5') 

EXEC sp_UseStringList @StringList