Final answer:
The limit of the function f(x) as x approaches 5 does not exist.
Therefore, the correct answer is: option 'DNE'.
Step-by-step explanation:
To find the limit of the function f(x) as x approaches 5, we need to examine the behavior of the function as x gets closer and closer to 5.
Looking at the table of values for f(x), we can see that as x approaches 5 from the left side (x < 5), the values of f(x) become increasingly negative, approaching -1000.
As x approaches 5 from the right side (x > 5), the values of f(x) become increasingly positive, approaching 1000.
Since the left-hand and right-hand limits are different, the overall limit does not exist.
Therefore, the answer is DNE (does not exist).