1. **State the problem:** We need to find five consecutive even integers whose sum is 470. 2. **Define variables:** Let the smallest even integer be $x$. 3. **Express the other integers:** Since they are consecutive even integers, the next ones are $x+2$, $x+4$, $x+6$, and $x+8$. 4. **Write the sum equation:** $$x + (x+2) + (x+4) + (x+6) + (x+8) = 470$$ 5. **Simplify the equation:** $$5x + (2+4+6+8) = 470$$ $$5x + 20 = 470$$ 6. **Solve for $x$:** $$5x = 470 - 20$$ $$5x = 450$$ $$x = \frac{450}{5} = 90$$ 7. **Answer:** The smallest integer is $\boxed{90}$.