Is it possible to have two numbers whose HCF is 25 and LCM is 520?

No, ∵ HCF does not divided LCM exactly

Using Euclid’s division lemma -

Take a = 520 and b = 25.

a = bq + r. where q is the quotient, r is the remainder and b is the divisor.

If HCF divides LCM completely, r = 0.

Here 520 = 25(20) + 20

So, r = 20

∵ r is not equal to zero

∴ HCF does not divides LCM completely.

So this is not possible for two numbers to have HCF = 25 and LCM = 520.