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$5^{10x} = (5^{5x})^{2}=4900$ . Therefore $5^{5x}=\sqrt{4900}=70$

Given $2^{\sqrt{y}}=5^{2}$ , we have that $4^{\sqrt{y}}=(2^{\sqrt{y}})^{2}=(5^{2})^{2}=5^4$

So, it is clear that $\frac{(5^{x-1})^5}{4^{-\sqrt{y}}} = \frac {\frac{5^{5x}}{5^{5}}}{\frac {1}{4^{\sqrt{y}}}} = =\frac{\frac{70}{5^{5}}}{\frac{1}{5^{4}}} = \frac{70 \times 5^{4}}{5^{5}} = \frac{70}{5} =14$

First thing one should notice here is that x and y must be some irrational numbers (4,900 has other primes then 5 in its prime factorization and 25 doesn't have 2 as a prime at all), so we should manipulate with given expressions rather than to solve for x and y.