It's actually not the hydroxymethelene group that determines the α/β status of a sugar, instead it's the relative orientation of the anomeric hydroxyl to the stereocenter which determines the absolute stereochemistry (D/L) of the sugar. This just so happens to match up with the same side/opposite side heuristic for the common six carbon pyranoses, but that's a quick rule of thumb, not the official definition:
α (alpha), β (beta): Relative stereodescriptors used in carbohydrate nomenclature to
describe the configuration at the anomeric carbon by relating it to
the anomeric reference atom. For simple cases the anomeric reference
atom is the same as the configurational reference atom. Thus in
α-d-glucopyranose the reference atom is C-5 and the OH at C-1 is on
the same side as the OH at C-5 in the Fischer projection.
IUPAC Gold Book
The configuration at the anomeric centre (that derived from the
carbonyl carbon) is denoted alpha- (α-) or beta- (β-) by reference to
the stereocentre that determines the absolute configuration. In a
Fischer projection, if the substituent off the anomeric centre is on
the same side as the oxygen of the configurational (D- or L-) carbon,
then it is the α--anomer. If it is directed in the opposite direction
it is the β-anomer.
CAZypedia - includes diagrams and examples, including for five carbon pyranoses.