Explanation:

Let's solve the equations:

1. Equation I: $x^2+31x+240=0$

- The factors are $(x+15)(x+16)=0$.

- So, the solutions are $x=-15$ and $x=-16$.

2. Equation II: $5y^2+60y+135=0$

- Dividing entire equation by 5 simplifies it to: $y^2+12y+27=0$.

- The factors of this equation are $(y+9)(y+3)=0$.

- So, the solutions are $y=-9$ and $y=-3$.

- Comparing values:

- $x=-15$ and $x=-16$ compared with $y=-9$ and $y=-3$.

- Check options:

- Option 1: x > y (False as x values are less than y values)

- Option 2: x < y (True as all x values are less than y values)

- Option 3: x = y (False)

- Option 4: x = y (True but less appropriate here)

- Option 5: x = y or no relationship (False)

The correct answer is Option 2: x < y