Square Properties: Analyzing a Quadrilateral with 5-Unit Sides

To determine if the quadrilateral $ABCD$ is a square, we need to verify two main criteria:

• All sides must be equal: The sides provided are $AB = BC = CD = DA = 5$. This condition is satisfied.
• All angles must be $90^\circ$: There is no clear indication or evidence presented in the problem that the angles are right angles.

Since we have confirmed that all sides are equal but lack the confirmation for all angles being $90^\circ$, we cannot assume $ABCD$ is a square. In a typical analysis without explicit angle data or additional geometric hints, equality of angles should not be assumed solely based on the visual diagram or equal sides.

Therefore, without concrete proof of all angles being $90^\circ$, the quadrilateral $ABCD$ is not definitively a square.

Therefore, the answer to the problem is "No".