On the non-orientable 4-genus of torus knots with braid index 5 or 6

The non-orientable 4-genus of a knot [Formula: see text] in [Formula: see text], denoted [Formula: see text], measures the minimum genus of a non-orientable surface in [Formula: see text] bounded by [Formula: see text]. We compute bounds for the non-orientable 4-genus of knots [Formula: see text] and [Formula: see text], extending previous research. Additionally, we provide a generalized, non-recursive formula for [Formula: see text], the [Formula: see text]-invariant of -1-surgery on torus knots.