Choice Bhoice C is the correct answer. We follow the two-step process: subtract, then divide.

1. Start with the equation: $5x + 10 = 35$
2. Subtract 10 from both sides: $5x = 35 - 10$
3. Simplify: $5x = 25$
4. Divide both sides by 5: $x = \frac{25}{5}$
5. Simplify: $x = 5$
6. Verify: $5(5) + 10 = 25 + 10 = 35$ ✓

Choice Bhoice A is incorrect because this results from adding 10 to 35: $35 + 10 = 45$, then $45/5 = 9$. This applies the wrong inverse operation.

Choice Bhoice D is incorrect because this is the value of $5x$. Don't forget the final division step!

Choice Bhoice D is incorrect because this might come from a calculation error, perhaps thinking $35 - 10 = 20$.