Find $d y$ for the given values of $x$ and $\Delta x$.
\[
y=x^{3}-7 x^{2}+5 ; x=1 ; \Delta x=-0.4
\]

Step 1 ：Given the function \(y=x^{3}-7 x^{2}+5\), the value of \(x=1\), and the change in \(x, \Delta x=-0.4\), we are asked to find the change in \(y, \Delta y\).

Step 2 ：We can solve this problem using the concept of derivatives. The derivative of a function gives us the rate of change of the function at a given point.

Step 3 ：First, we need to find the derivative of the function \(y=x^{3}-7 x^{2}+5\). The derivative of this function is \(dy/dx = 3x^{2}-14x\).

Step 4 ：Next, we evaluate the derivative at the given x value, \(x=1\). Substituting \(x=1\) into the derivative, we get \(dy/dx = 3(1)^{2}-14(1) = -11\).

Step 5 ：Finally, we multiply the derivative at the given x value by the change in x to find the change in y. So, \(\Delta y = dy/dx \times \Delta x = -11 \times -0.4 = 4.4\).

Step 6 ：Thus, the change in y, given the function \(y=x^{3}-7 x^{2}+5\), the x value of 1, and the change in x of -0.4, is \(\boxed{4.4}\).