Solve for x: $x^3-\lfloor x\rfloor=5$ 
Solve for x:$$x^3-\lfloor x\rfloor=5$$

My Attempt:
$x^3-5=\lfloor x\rfloor$
Now, $x-1<\lfloor x\rfloor\leq x$
$x-1<x^3-5\leq x$
Not able to proceed from here

Consider the three functions $ y = x-1 $, $ y = x ^ 3-5 $ and $ y = x $. Compare the portion of the graph of $ y = x ^ 3-5 $ that is between the graphs of $ y = x-1 $ and $ y = x $. What can you say about that?
The possible solutions of the equation $x^3-\lfloor x\rfloor=5 $ live in the set of solutions of the inequation $x-1<x^3-5\leq x$.
From the graph we can see that all solutions of the equation $x^3-\lfloor x\rfloor=5 $ are larger than the only real root of $x^3-5= x-1$ and less than the only real root of $x^3-5=x$.
