Factor completely \[ 5 h^{2}-40 h+75 \]

To factor the quadratic expression \( 5 h^{2} - 40 h + 75 \), we first look for a common factor in all the terms, which is 5. Factoring out 5 gives us: \[ 5(h^{2} - 8h + 15) \] Next, we focus on factoring the quadratic \( h^{2} - 8h + 15 \). We need to find two numbers that multiply to 15 and add up to -8. The numbers -3 and -5 fit the criteria, therefore we can factor it as follows: \[ h^{2} - 8h + 15 = (h - 3)(h - 5) \] Putting it all together, we get: \[ 5(h - 3)(h - 5) \] So, the completely factored form is: \[ 5(h - 3)(h - 5) \]