Step 1: Express both sides of the equation with the same base.

$$5^{2(3x-5)} = 5^1$$ $$5^{6x-10} = 5^1$$

$$6x = 1 + 10$$ $$6x = 11$$ $$x = \frac{11}{6}$$

The value of $x$ is:

$$\boxed{\frac{11}{6}}$$

9. Step 1: Rewrite the expression using reciprocals. The expression is $\frac{5}{0.6699} - \frac{1}{4.231}$. This can be written as $5 \times \frac{1}{0.6699} - \frac{1}{4.231}$.

Using a calculator to simulate reciprocal table values:

$$\frac{1}{0.6699} \approx 1.4928$$ $$\frac{1}{4.231} \approx 0.2364$$

$$5 \times 1.4928 - 0.2364$$ $$7.4640 - 0.2364$$ $$7.2276$$

The evaluated expression is:

$$\boxed{7.2276}$$

10. Step 1: Evaluate the logarithm. The given equation is $\log 0.00001 = 2y$. Assuming the base of the logarithm is 10 (common for "log" when no base is specified). First, express 0.00001 as a power of 10:

$$0.00001 = 10^{-5}$$

Now, evaluate $\log_{10} (10^{-5})$:

$$\log_{10} (10^{-5}) = -5$$

Substitute the value of the logarithm back into the given equation:

$$-5 = 2y$$

Divide by 2 to find $y$:

$$y = \frac{-5}{2}$$ $$y = -2.5$$

The value of $y$ is:

$$\boxed{-2.5}$$