Place real numbers at the vertices of a pentagon so that the sum of the numbers at the ends of one side is equal to 1, at the ends of another side is equal to 2, ..., and at the ends of the last side is equal to 5.

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Place the number $x$ at the 1st vertex, $1-x$ at the 2nd, $1+x$ at the 3rd, $-2-x$ at the 4th, and $-2+x$ at the 5th. Then, for any value of $x$, the sums of the numbers on the four sides will be 1, 2, 3, and 4, respectively. To make the sum of the numbers on the 5th side equal to 5, we need to find $x$ from the condition $x+(2+x)=5$. Hence, $x=1.5$.

## Answer

$3 / 2, -1 / 2, 5 / 2, 1 / 2, 7 / 2$.