Calculate Test Points: 5 for Correct, -2 for Wrong, -4 for Unattempted Answers

To solve this problem, we'll follow these steps:

• Step 1: Calculate the points from the correct answers
• Step 2: Calculate the points from the incorrect answers
• Step 3: Calculate the points for the unattempted questions
• Step 4: Sum all the points to find the final score

Now, let's work through each step:

Step 1: The student answered 15 questions correctly.
The points from correct answers are calculated as follows:
$5 \times 15 = 75$ points.

Step 2: The student answered 2 questions incorrectly.
The points from incorrect answers are calculated as follows:
$-2 \times 2 = -4$ points.

Step 3: The student left 3 questions unattempted.
The points from unattempted questions are calculated as follows:
$-4 \times 3 = -12$ points.

Step 4: Add all the points from the above scenarios:
Total points = (Points from correct answers) + (Points from incorrect answers) + (Points from unattempted questions)
Total points = $75 + (-4) + (-12) = 75 - 4 - 12 = 59$.

Therefore, the student's final score is $59$.