1. **State the problem:** Find the intersection point of the two lines given by the equations: $$2x = y + 5$$ and $$6x + 2y = -5$$ 2. **Rewrite the first equation to express $y$ in terms of $x$: ** $$2x = y + 5 \implies y = 2x - 5$$ 3. **Substitute $y = 2x - 5$ into the second equation:** $$6x + 2(2x - 5) = -5$$ 4. **Simplify the equation:** $$6x + 4x - 10 = -5$$ $$10x - 10 = -5$$ 5. **Add 10 to both sides:** $$10x - 10 + 10 = -5 + 10$$ $$10x = 5$$ 6. **Divide both sides by 10:** $$\cancel{10}x = \frac{5}{\cancel{10}}$$ $$x = \frac{1}{2}$$ 7. **Substitute $x = \frac{1}{2}$ back into $y = 2x - 5$ to find $y$: ** $$y = 2 \times \frac{1}{2} - 5 = 1 - 5 = -4$$ 8. **Conclusion:** The lines intersect at the point $$\left(\frac{1}{2}, -4\right)$$. **Answer:** $\boxed{\left(\frac{1}{2}, -4\right)}$