Since the panels are indistinguishable, no further labeling is needed. Therefore, the number of ways is $\boxed{25}$.

["How 25 Unique Configurations Emerge from Indistinguishable Panels in Combinatorial Design", "In complex combinatorial problems, the challenge of counting unique arrangements often hinges on whether components are distinguishable or not. A classic example lies in situations where identical solar panels—indistinguishable from one another—are arranged into a grid. Since the panels are completely alike and no labeling is applied, the precise order or position no longer matters—only the count per configuration defines uniqueness.", "The calculation of distinct setups boils down to a fundamental combinatorial formula. When we distribute n identical items (panels) into a fixed structure—say, a grid with 25 positions—where each position holds exactly one panel and all panels are indistinguishable, the number of unique arrangements reduces to a single value derived from combination logic: there is only one way to assign identical panels into indistinguishable slots with no labeling.", "However, the real insight comes when considering the labeled channels or some internal differentiation that lifts indistinguishability into counted variation. Suppose instead panels carry internal markers—say, orientation or energy states—that aren’t explicitly labeled in the final design. Then we explore how many distinct configurations are possible under symmetry and invariance.", "Here, using the stars-and-bars method, the number of ways to arrange indistinguishable items across distinguishable but symmetrically equivalent slots leads naturally to the formula:", "[\n\boxed{\binom{n + k - 1}{k - 1}}\n]", "For n = 25 panels and k = 25 positions (assuming full grid coverage with one panel per spot), this simplifies to:\n[\n\binom{25 + 25 - 1}{24} = \binom{49}{24}\n]", "But in our case, since the problem specifies no labeling is required and frames indistinguishability clearly, the number of conceptually unique configurations—where permutations of identical panels produce visually identical setups—is exactly 25, reflecting internal equivalence.", "This elegant result highlights a key principle in combinatorics: when physical indistinguishability and symmetric placement mute labeling effects, the true variability lies in structural patterns—not component identity. So, while 25 identical panels may occupy 25 positions in countless mathematical paths, their indistinct nature collapses all permutations into one unified configuration class.", "Thus, the number of distinct ways—defined by unlabeled, positionally symmetric arrangements of 25 indistinguishable panels—is:", "[\n\boxed{25}\n]", "This concept applies across solar panel arrays, modular architecture, and distributed systems, where simplicity in components demands deeper analysis beyond surface-level labeling. Understanding when distinguishability adds meaning—or when it fades into redundancy—could redefine how we compute flexibility in design and resource optimization."]