When a polynomial is divided by (x-5) the quotient is 5x↑2+3x+12 with the remainder 7. find the polynomial

First I will present the polynomial itself:  it is 

5x^3 - 22x^2 - 3x - 53.  

Let's show that when this poly. is divided by (x-5), the quotient is 5x^2 + 3x + 12 and the remainder is 7.  Use synthetic division here.  Let the divisor be 5 (this comes from the factor (x-5).  Then:
     
5  /  5   -22   -3   -53
             25    15   60
     
       5      3    12    7      where 5  3  12 are the coeff. of the quotient and 7
                                      is the remainder.

Now work backwards.  Multiply (x-5) and (5x^2 + 3x + 12) together.  We get 

      5x^3 + 3x^2 + 12 x - 25x^2 - 15x - 60, or

       5x^3 - 22x^2 - 3x - 60.  Now add the remainder (7) to -60; the result will be -53.  

So the poly in question is 5x^3 - 22x^2 - 3x - 53.

Idon’t know this and this isn’t middle school work