If a -1/(a-5)= 10, then the value of (a — 5)^3 -1/((a-5)^3) is:

If $a -\frac{1}{a-5}= 10$

then the value of $(a — 5)^3 -\frac{1}{(a-5)^3}$  = ?

Subtract 5 on both sides ,

$a - 5 -\frac{1}{a-5}= 10 - 5$

If $a - 5-\frac{1}{a-5}= 5$

If x - \(\frac{1}{x}\)  = n

then, $x^3 -\frac{1}{x^3}$ = n³ + 3 × n

So, $(a — 5)^3 -\frac{1}{(a-5)^3}$  = 5³ + 3 × 5 = 125 + 15 = 140