Differentiate implicitly to find $\frac{d^{2} y}{d x^{2}}$.
\[
3 x^{3}-4 y^{3}=5
\]

Step 1 ：Given the equation \(3x^{3} - 4y^{3} = 5\), we first differentiate both sides with respect to \(x\).

Step 2 ：Differentiating \(3x^{3}\) with respect to \(x\) gives \(9x^{2}\).

Step 3 ：Differentiating \(-4y^{3}\) with respect to \(x\) gives \(-12y^{2} \frac{dy}{dx}\) by the chain rule.

Step 4 ：Differentiating \(5\) with respect to \(x\) gives \(0\).

Step 5 ：So, the derivative of the given equation is \(9x^{2} - 12y^{2} \frac{dy}{dx} = 0\).

Step 6 ：Rearranging for \(\frac{dy}{dx}\), we get \(\frac{dy}{dx} = \frac{9x^{2}}{12y^{2}} = \frac{3x^{2}}{4y^{2}}\).

Step 7 ：Next, we differentiate \(\frac{dy}{dx}\) with respect to \(x\) to find \(\frac{d^{2} y}{d x^{2}}\).

Step 8 ：Differentiating \(\frac{3x^{2}}{4y^{2}}\) with respect to \(x\) using the quotient rule gives \(\frac{d^{2} y}{d x^{2}} = \frac{4y^{2}(6x) - 3x^{2}(8y \frac{dy}{dx})}{(4y^{2})^{2}}\).

Step 9 ：Substituting \(\frac{dy}{dx} = \frac{3x^{2}}{4y^{2}}\) into the equation, we get \(\frac{d^{2} y}{d x^{2}} = \frac{4y^{2}(6x) - 3x^{2}(8y \frac{3x^{2}}{4y^{2}})}{(4y^{2})^{2}}\).

Step 10 ：Simplifying the equation, we get \(\frac{d^{2} y}{d x^{2}} = \frac{24xy^{2} - 18x^{3}y}{16y^{4}} = \frac{6x(y^{2} - 3x^{2})}{4y^{4}} = \frac{3x(y^{2} - 3x^{2})}{2y^{4}}\).

Step 11 ：So, the second derivative of \(y\) with respect to \(x\) is \(\boxed{\frac{3x(y^{2} - 3x^{2})}{2y^{4}}}\).