Note that all the twisted knots are “alternating”. That is, if you trace the path of the knot, the underpasses and overpasses alternates.
When the 5-2-knot is twisted in one direction we find new knots where overpasses and underpasses alternate. These alternating knots cannot be drawn with fewer crossings. Twisting in the other direction gives knots with two consecutive underpasses, these can probably be simplified.