1. **State the problem:** Simplify the expression $5 \cdot x^3 - 8x + 2y + x + 2$. 2. **Combine like terms:** Group the terms with $x^3$, $x$, $y$, and constants separately. 3. The term with $x^3$ is $5x^3$. 4. The terms with $x$ are $-8x$ and $+x$. Combine them: $$-8x + x = -7x$$ 5. The term with $y$ is $2y$. 6. The constant term is $2$. 7. **Write the simplified expression:** $$5x^3 - 7x + 2y + 2$$ This is the simplified form of the given expression. **Final answer:** $5x^3 - 7x + 2y + 2$