Determine the values of f(x) when x is less than -3:
$f(x)=\{\begin{array}{ll}-3x+5& \text{ if }x<-3\\ 5& \text{ if }-3\le x\le 3\\ -x+14& \text{ if }x>3\end{array}$

Step 1 ：We are given the piecewise function $f(x)=\{\begin{array}{ll}-3x+5& \text{ if }x<-3\\ 5& \text{ if }-3\le x\le 3\\ -x+14& \text{ if }x>3\end{array}$

Step 2 ：We are asked to determine the values of $f(x)$ when $x$ is less than $-3$. From the given function, we can see that when $x$ is less than $-3$, the function is defined as $-3x+5$.

Step 3 ：Let's calculate the value of $-3x+5$ for $x<-3$.

Step 4 ：We can plot the function $f(x)$ for $x$ in the interval $[-10,-3]$ to visualize the values of $f(x)$.

Step 5 ：From the plot, we can see that as $x$ decreases, $f(x)$ increases linearly. The values of $f(x)$ range from $5$ to $35$ when $x$ is in the interval $[-10,-3]$.

Step 6 ：$\boxed{{\displaystyle \text{Final Answer: The values of }f(x)\text{ when }x\text{ is less than }-3\text{ are given by the function }-3x+5.\text{ The values of }f(x)\text{ range from }5\text{ to }35\text{ when }x\text{ is in the interval }[-10,-3].}}$