This is exactly what you get.

Two rules are running at once and they have different cycle lengths, so the reliable method is to run each one on its own clock rather than trying to picture the combined shape. Rotation first: five steps of 90° is 450°, which is one full turn plus another 90. The cycle completes at step four, not step five, so the shape is not back where it started. It sits one quarter-turn on. That off-by-one is what catches most people, because four steps feels like the natural stopping point. The flip is a separate clock entirely: it fires on steps two and four only, which is two flips, and two vertical flips return a shape to the orientation it began in. So by step five there is no flip in effect at all, even though flips did happen along the way. Rotation and flip resolve independently, which is the whole point of the question.

This one catches almost everybody, because the conclusion sounds so reasonable. All club members are chess players, and some chess players compete nationally, but nothing guarantees the overlap falls inside the club. The nationally competing players could all be people from outside it. For a syllogism like this to work, the "some" statement has to start from the group you are reasoning about, not the larger group it sits inside. Ask yourself whether you could draw the diagram with zero overlap and still satisfy every premise. If you can, it is invalid.