To express \(5y^2 - 30y + 50\) in the form \(5(y + a)^2 + b\), follow these steps:

1. Start with the expression: \(5y^2 - 30y + 50\).

2. Factor out 5 from the first two terms: \(5(y^2 - 6y) + 50\).

3. Complete the square inside the parentheses:

- Take half of the coefficient of \(y\), which is \(-6\), to get \(-3\).

- Square \(-3\) to get 9.

4. Add and subtract 9 inside the parentheses:

\(5(y^2 - 6y + 9 - 9) + 50\).

5. Rewrite the expression as:

\(5((y - 3)^2 - 9) + 50\).

6. Distribute the 5:

\(5(y - 3)^2 - 45 + 50\).

7. Simplify the constants:

\(5(y - 3)^2 + 5\).

Thus, \(a = -3\) and \(b = 5\).