Question 193147
Let x = the dimension of one side of the original cube.  Its volume is {{{V[c] = x^3}}}
The three sides of the new solid are: x, (x-1), and (x+1).
The volume of the new solid is:
{{{V[n] = (x)(x-1)(x+1)}}}
{{{V[n] = x^3-x}}} and this is said to be equal to five less than that of the cube, or {{{x^3-5}}}, so....
{{{x^3-x = x^3-5}}} Subtract {{{x^3}}} from both sides.
{{{-x = -5}}} or
{{{x = 5}}}
The volume of the cube is then...
{{{V[c] = x^3}}} substitute x = 5.
{{{V[c] = 5^3}}}
{{{highlight(V[c] = 125)}}} cubic units.