MSSQL Geography STIntersects returns 1 when 0 is expected
The reason you are having a problem is that the polygon is wound the wrong way which results in a polygon that covers the entire world except for your area of interest.

Try

DECLARE @t_point geography;  
DECLARE @t_polygon geography;
set @t_polygon = geography::STPolyFromText('POLYGON((1 1, 5 0, 5 5, 1 1))', 4326);
set @t_point = geography::Point(0, 0, 4326);


It is a bit strange, but given that with geographies we are dealing with a sphere, there needs to be a way to determine which side of the boundary is the interior of the polygon.  With SQL Server, this is done by making the exterior boundary be defined as anti clockwise.

Geometries don't care which way they are wound, but prefer anti clockwise.  There is a function for geographies ReorientObject that change the direction of the object.