5. (10 points) A store sold some pens on the first day. On the second day, after reducing the price of each pen by 1 yuan, it sold 100 more pens. On the third day, after increasing the price of each pen by 3 yuan compared to the previous day, it sold 200 fewer pens than the previous day. If the store made the same amount of money each day, what was the price of each pen on the first day? $\qquad$ yuan.

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【Analysis】Let the price of each pen on the first day be $x$ yuan, and the number sold be $y$ pens. According to the formula total price = unit price $\times$ quantity, the amount of money made on the first day is $x y$ yuan. The unit price on the second day is $x-1$ yuan, and the number of pens sold is $y+100$ pens, so the total price on the second day is $(x-1)(y+100)$. Similarly, we can derive the total price for the third day. We then set up a system of equations based on the equality of the amount of money made on the first day and the amounts made on the second and third days, and solve the equations after simplification.

【Solution】Solution: Let the unit price on the first day be $x$ yuan, and the quantity be $y$ pens, then we have:
$$
\left\{\begin{array}{l}
(x-1)(y+100)=x y \\
(x-1+3)(y+100-200)=x y
\end{array}\right.
$$

Simplifying, we get:
$$
\left\{\begin{array}{l}
100 x-y=100 \\
2 y-100 x=200
\end{array}\right.
$$

Solving, we get:
$$
\left\{\begin{array}{l}
x=4 \\
y=300
\end{array}\right.
$$

Answer: The price of each pen on the first day is 4 yuan.
Therefore, the answer is: 4.