[THOUGHT] To find the area of triangle ABC, we use the formula: Area = (1/2) * AB * AC * sin(angle BAC). Given AB = 5, AC = 6, and cos(angle BAC) = -3/5, we first compute sin(angle BAC) using the identity sin²θ + cos²θ = 1. Since cos is negative, the angle is obtuse, so sin is positive. Then we calculate the area using these values. [/THOUGHT] [PYTHON] from sympy import Rational, sqrt

Given values

AB = Rational(5) AC = Rational(6) cos_angle = Rational(-3, 5)

Compute sin(angle BAC)

sin_angle = sqrt(1 - cos_angle**2)

Compute area

area = Rational(1, 2) * AB * AC * sin_angle print(area) [/PYTHON]

[THOUGHT] The area calculation was verified using the formula (1/2) * AB * AC * sin(angle BAC). With AB=5, AC=6, and sin(angle BAC)=4/5 derived from cos(angle BAC)=-3/5, the area is 12. The Python output confirms this result. [/THOUGHT] \boxed{12}