I've been asked to: use determinant properties to evaluate the 5 x 5 determinant given below.

I've only just started learning matrix algebra, but I was aiming to reduce this matrix to a triangle matrix so I could use the main diagonal to calculate the determinant. I have a couple of questions though:

1 - Does this method count as "using determinant properties"? Or should I be doing it differently in order to answer the question correctly?

2 - Is my working below (and resulting determinant) correct?

WORKING STEPS:

1 - Add the first row to the second.

2 - Subtract 2x the first row from the fourth.

3 - Add 2x the fifth row to the fourth.

4 - Subtract 1/4x the third row from the fifth.

Because this is now a triangle matrix, the determinant should just be equal to the multiple of the main diagonal right? i.e. 1 x 5 x 4 x -24 x 3 = -1440

I have a strong feeling that this is wrong, and possibly that the 0 5 0 0 0 row is more significant than I realise. Any comments/help would be greatly appreciated.