The last term of an arithmetic progression is equal to the number of its terms. The difference of the progression is 5, and its sum is -6. Which is this progression?
If the first term of the arithmetic sequence is $a$, the number of terms, and the last term is $n$, then according to the problem:

$$
n=a+(n-1) 5
$$

and

$$
-6=\frac{n}{2}(a+n)
$$

from which:

$$
3 n^{2}-5 n-12=0
$$

from which the positive root is:

$$
n=3
$$

and from (1):

$$
a=-7
$$

the arithmetic sequence is:

$$
-7,-2,3
$$

Number of solutions: 71.