1. **State the problem:** We have two numbers, let's call the larger number $x$ and the smaller number $y$. 2. **Translate the problem into equations:** - "Thrice the larger of two numbers is five more than five times the smaller" translates to: $$3x = 5y + 5$$ - "The sum of six times the larger and five times the smaller is 265" translates to: $$6x + 5y = 265$$ 3. **Solve the system of equations:** From the first equation, express $3x$: $$3x = 5y + 5$$ Divide both sides by 3: $$x = \frac{5y + 5}{3}$$ 4. Substitute $x$ in the second equation: $$6 \left(\frac{5y + 5}{3}\right) + 5y = 265$$ Simplify: $$2(5y + 5) + 5y = 265$$ $$10y + 10 + 5y = 265$$ $$15y + 10 = 265$$ 5. Solve for $y$: $$15y = 265 - 10$$ $$15y = 255$$ $$y = \frac{255}{15} = 17$$ 6. Find $x$ using $y = 17$: $$x = \frac{5(17) + 5}{3} = \frac{85 + 5}{3} = \frac{90}{3} = 30$$ 7. **Answer:** The larger number is $\boxed{30}$.