Final answer:
To translate the function y = 5/x four units to the left and three units up, the new equation is y = 5/(x + 4) + 3.
Step-by-step explanation:
The original equation of the function is y = 5/x. When you translate this function 4 units to the left, you replace x with (x + 4), since moving left on the x-axis means subtracting from x, and you do the opposite for the transformation. When you translate it 3 units up, you add 3 to the entire function, hence the new equation for y after translating it would be y = 5/(x + 4) + 3.