To evaluate the given expression [tex]\([c+7(d-3)]^2 \div 3\)[/tex] for the values [tex]\(a=5, b=3, c=7, d=5\)[/tex], follow these steps:
1. Simplify the Innermost Expression:
[tex]\[
d - 3
\][/tex]
Substitute [tex]\( d = 5 \)[/tex]:
[tex]\[
5 - 3 = 2
\][/tex]
2. Multiply by 7:
[tex]\[
7 \times (d - 3) = 7 \times 2 = 14
\][/tex]
3. Add [tex]\(c\)[/tex]:
[tex]\[
c + 7(d - 3) = 7 + 14 = 21
\][/tex]
4. Square the Result:
[tex]\[
[c + 7(d - 3)]^2 = 21^2 = 441
\][/tex]
5. Divide by 3:
[tex]\[
\frac{[c + 7(d - 3)]^2}{3} = \frac{441}{3} = 147
\][/tex]
So, the step-by-step evaluation shows that the final result of the given expression is:
[tex]\[
147
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{147}\)[/tex].
