5. (10 points) The product of two decimal numbers, when rounded to the nearest tenth, is 27.6. It is known that both decimals have one decimal place and their units digits are both 5. What is the exact product of these two decimals? $\qquad$ .
【Analysis】First, based on the unit digit being 5, the unit digit of the product of two 5s must also be 5. Then, according to the rules of rounding, the solution can be found.
【Solution】Solution: According to the problem, we know:
First, based on the result of the multiplication of two decimals being a 2-digit decimal, and the unit digits being 5, the original result's last digit must be 5; according to the rounded result being 27.6, the only value that satisfies the condition is 27.55.

Therefore, the answer is: 27.55