Does anyone know why this is wrong? I listed step by step what I did.

Find the following determinants by cofactor expansion along a convenient row or columns

|5 -1 5 0 -3 |

|4 0 3 -2 2 |

|3 2 1 0 3 |

|7 0 -3 0 4 |

|2 -1 4 3 -2 |

First, I took R5 ->2R5+3R2

I then got

|-5 -1 5 -0 -3|

|4 0 4 -2 2|

|3 2 1 0 3 |

|7 0 -3 0 4 |

|16-2 17 0 2 |

I then got -2 as a cofactor and used that as a pivot so i have -2 * the matrix below.

|-5 -1 5 -0 -3|

|3 2 1 0 3 |

|7 0 -3 0 4 |

|16-2 17 0 2 |

I then performed the following row operations:

R1-> 2R1 + R2

R4 -> R4 + R2 and I get

|-7 0 11 -3|

|3 2 1 3|

|7 0 -3 4|

|19 0 18 5|

I used the row 3,2,1,3 as the pivot and I have the resulting matrix

-4 cofactor times

|-7 11 -3|

|7 -3 4|

|19 18 5|

If I just take the value of the determinant 3 x 3 I get the correct answer, but shouldn't i multiply the matrix by -4? Intuitively I feel like it should be multiplied by -5. Any thoughts?