8. (10 points) In the figure, the five Chinese characters “华罗庚金杯” represent five different digits from $1-5$. By adding the numbers at the endpoints of each line segment, five sums are obtained. There are $\qquad$ ways to make these five sums exactly five consecutive natural numbers.
【Analysis】According to “the sum of the numbers at the endpoints of each line segment is exactly 5 consecutive natural numbers,” it can be seen that these 5 sums are somewhat larger than the original $1, 2, 3, 4, 5$; the numbers at the 5 vertices of the pentagram are counted twice, so the total sum of the 5 sums can be calculated as: $2 \times (1+2+3+4+5)=30$, the sum of the original 5 natural numbers is: $1+2+3+4+5=15$, the new 5 consecutive natural numbers are more than the original 5 consecutive natural numbers by: $30-15=15$, on average each is more by $15 \div 5=3$, then the new 5 consecutive natural numbers are: $1+3, 2+3, 3+3, 4+3, 5+3$, which are $4, 5, 6, 7, 8$; then combining the smallest and largest natural numbers, the number of possible values for each vertex can be determined, and the total number of cases can be determined.

【Solution】Solution: The numbers at the 5 vertices of the pentagram are counted twice, so the total sum of the 5 sums can be calculated as: $2 \times$
$$
(1+2+3+4+5)=30,
$$

the sum of the original 5 natural numbers is: $1+2+3+4+5=15$,
the new 5 consecutive natural numbers are more than the original 5 consecutive natural numbers by: $30-15=15$,
on average each is more by $15 \div 5=3$,
then the new 5 consecutive natural numbers are: $1+3, 2+3, 3+3, 4+3, 5+3$, which are $4, 5, 6, 7, 8$;
observing these new 5 consecutive natural numbers, the smallest natural number 4 can only be $4=1+3$, the largest natural number 8 can only be $5+3$,
and 2 cannot be paired with 1, 4 cannot be paired with 5, thus there are the following combinations: since each vertex has 2 different possible values, there are a total of $2 \times 5=10$ cases; Answer: There are 10 cases in total that make these five sums exactly five consecutive natural numbers. Therefore, the answer is: 10.