Five Numbers

I wrote down five numbers.
The first number is 1,
the product of the first two is 2,
the product of the first three is 3,
the product of the first four is 4, and
the product of the first five is 5.

What is the sum of the five numbers?

Let your answer be the improper fraction $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers. Submit $a + b$ .