For the piecewise linear function, find $(a) f(-4),(b) f(-2)$, (c) $f(0)$, (d) $f(3)$, and $(e) f(5)$. \[ f(x)=\left\{\begin{array}{ll} 2 x & \text { if } x \leq-2 \\ x-2 & \text { if } x>-2 \end{array}\right. \]

Step 1 ：We are given a piecewise linear function, \(f(x)\), which is defined as follows: \[f(x)=\left\{\begin{array}{ll} 2x & \text { if } x \leq -2 \\ x-2 & \text { if } x > -2 \end{array}\right.\]

Step 2 ：We need to find the values of the function at different points: \(-4, -2, 0, 3, 5\).

Step 3 ：Let's start with \(f(-4)\). Since \(-4\) is less than \(-2\), we use the first part of the function definition: \(2x\). Substituting \(-4\) for \(x\), we get \(2*(-4) = -8\). So, \(f(-4) = -8\).

Step 4 ：Next, let's find \(f(-2)\). Since \(-2\) is equal to \(-2\), we use the first part of the function definition: \(2x\). Substituting \(-2\) for \(x\), we get \(2*(-2) = -4\). So, \(f(-2) = -4\).

Step 5 ：Now, let's find \(f(0)\). Since \(0\) is greater than \(-2\), we use the second part of the function definition: \(x-2\). Substituting \(0\) for \(x\), we get \(0-2 = -2\). So, \(f(0) = -2\).

Step 6 ：Next, let's find \(f(3)\). Since \(3\) is greater than \(-2\), we use the second part of the function definition: \(x-2\). Substituting \(3\) for \(x\), we get \(3-2 = 1\). So, \(f(3) = 1\).

Step 7 ：Finally, let's find \(f(5)\). Since \(5\) is greater than \(-2\), we use the second part of the function definition: \(x-2\). Substituting \(5\) for \(x\), we get \(5-2 = 3\). So, \(f(5) = 3\).

Step 8 ：Summarizing, we have: \(f(-4) = \boxed{-8}\), \(f(-2) = \boxed{-4}\), \(f(0) = \boxed{-2}\), \(f(3) = \boxed{1}\), and \(f(5) = \boxed{3}\).