An angle, θ, is in standard position. the terminal side of the angle passes through the point (-5, -3). find tanθ.

If the terminal ray of an angle passes through (-5, -3), that means it passes through x coordinate -5 and y coordinate -3.  Both x and y are negative in only one quadrant and that is the third one.  If we plot the point (-5, -3) in the coordinate plane in Q3, and then draw a vertical line to connect that point to the negative x axis and then draw a line to connect that point to the origin, what we have created is right triangle with a base of -5 and a height of -3. The tangent ratio relates the side opposite the reference angle to the side adjacent to the reference angle.  We have both of those measures already and do not have a need for the length of the hypotenuse since the tangent ratio doesn't use it.  The tangent of the reference angle is -3/-5 which is 3/5.