Find (A) the leading term of the polynomial, (B) the limit as $x$ approaches $\infty$, and (C) the limit as $x$ approaches $-\infty$.
\[
p(x)=5 x+x^{3}-7 x^{2}
\]

Step 1 ：Identify the leading term of the polynomial \(p(x)=5x + x^{3} - 7x^{2}\). The leading term is the term with the highest degree.

Step 2 ：The leading term of the polynomial is \(x^{3}\).

Step 3 ：Determine the limit of the polynomial as \(x\) approaches \(\infty\) and \(-\infty\). This is determined by the leading term.

Step 4 ：As \(x\) gets very large (either positively or negatively), the term with the highest degree will dominate the polynomial. Therefore, the limit as \(x\) approaches \(\infty\) or \(-\infty\) will be the same as the limit of the leading term as \(x\) approaches \(\infty\) or \(-\infty\).

Step 5 ：The limit as \(x\) approaches \(\infty\) is \(\infty\).

Step 6 ：The limit as \(x\) approaches \(-\infty\) is \(-\infty\).

Step 7 ：Final Answer: (A) The leading term of the polynomial is \(\boxed{x^{3}}\). (B) The limit as \(x\) approaches \(\infty\) is \(\boxed{\infty}\). (C) The limit as \(x\) approaches \(-\infty\) is \(\boxed{-\infty}\).