Compare the prime factorizations:
25 • 5 • 11 = 5² • 5 • 11 = 5³ • 11
23 • 52 • 7 = 23 • (2² • 13) • 7 = 2² • 7 • 13 • 23
Clearly these products have no common prime factors, so their GCF is 1.
But I'm guessing this a multiple choice question, and the numbers you listed are already prime factorizations. In that case, we have
2⁵ • 5 • 11 = 2³ • 2² • 5 • 11
2³ • 5² • 7 = 2³ • 5 • 5 • 7
with the common factors underlined, so that the GCF is 2³ • 5.
