Final answer:
The equation |a - 5| = -3 has no solutions because an absolute value cannot be negative.
Step-by-step explanation:
The question asks how many solutions does the equation |a – 5| = -3 have. An absolute value expression, like |a – 5|, is always non-negative, meaning it can never be less than zero. Therefore, it is impossible for it to be equal to a negative number, like -3. Since there is no value of 'a' that would satisfy this equation, the equation has no solutions.