Floor function equation

In order for the equation to be true, $5 - \left\lfloor x \right\rfloor$ must be greater than or equal to $15$ and less than but not equal to $16$ i.e.

$15 \le 5 - \left\lfloor x \right\rfloor < 16$

$10 \le - \left\lfloor x \right\rfloor < 11$

$-11 < \left\lfloor x \right\rfloor \le -10$ .

Since $\left\lfloor x \right\rfloor$ is an integer, $\left\lfloor x \right\rfloor = -10$ , as this is the only integer in the interval $(-11,-10]$ .

$x$ must therefore be greater than or equal to $-10$ and less than but not equal to $-9$ i.e. $-10 \le x < -9$ .

$a=-10$ , $b=-9$ , $ab=\boxed {90}$ .

Let $y$ $=$ $\left\lfloor x \right\rfloor$

As $y$ is an integer so
$\left\lfloor 5 - y \right\rfloor$ $=$ $5 - y$ $=$ $10$ $\Rightarrow$ $y = -10$

For any $-10 \le x \lt -9$ $,$ $\left\lfloor x \right\rfloor$ $=$ $-10$

So here $(a = -10,b = -9)$ $ab = (-10)(-9) = \boxed{90}$