To determine the value of [tex]\(\frac{a^3 - b^3}{5}\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -3\)[/tex], let's walk through the calculation step-by-step.
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[
a^3 = (2)^3 = 2 \times 2 \times 2 = 8
\][/tex]
2. Calculate [tex]\(b^3\)[/tex]:
[tex]\[
b^3 = (-3)^3 = (-3) \times (-3) \times (-3) = -27
\][/tex]
3. Calculate the numerator [tex]\(a^3 - b^3\)[/tex]:
[tex]\[
a^3 - b^3 = 8 - (-27) = 8 + 27 = 35
\][/tex]
4. Divide the result by 5:
[tex]\[
\frac{a^3 - b^3}{5} = \frac{35}{5} = 7
\][/tex]
Therefore, the value of the expression [tex]\(\frac{a^3 - b^3}{5}\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -3\)[/tex] is [tex]\(7\)[/tex].
The correct answer is:
[tex]\[
\boxed{7}
\][/tex]
