The sequence [m]x_1, x_2[/m]... [m]x_n[/m] is such that [m]x_1[/m] = 5

The sequence is {5,-5,0,-2,4,5,-5,0,-2,4....}

The first 5 consecutive terms give us sum as 5+(-5)+0+(-2)+4=2
So every 5 consecutive terms thereafter will give a sum 2.

(1) Sum of the first P terms in the given sequence is 10
Since each set of 5 consecutive terms gives a sum 2. Sum of 5 such sets will surely give as sum as 10.
Thus 25 terms. But are there any more ways
26th and 27th terms are 5 and -5 and will add nothing, so P can be 27.
Thereafter 28th term is 0, so again P can be 28.
What about the role -2 can play? If our sum is 12, and we add -2, we again get 10.
6 sets give us 12 as the sum and when we add another 4 terms(whose sum is 5+-5+0+-2 or -2), the sum is again 10. So P can be 5*6+4=34
Insufficient

(2) Sum of the first P+3 terms in the given sequence is 10
We know the sum is 10, when there are any of the number of the terms: 25, 27, 28, or 34.
P+3 can be any of these and accordingly P will differ.
Insufficient


Combined
P and P+3 both give sum as 10.
25, 27, 28, 34
Only 25 and 28 fit in for value of P and P+3.
Sufficient


C