2015 AMC 10B Problem 10

There are $1007$ odd numbers greater than $-2015.$ Our product is of an odd number of negative numbers, so the result is negative. Also, we multiply by $-5$ in there, so the product is a multiple of $5,$ making it end in $5$ or $0.$ None of our factors are even, so the product can’t be even. Therefore, the product must end in $5.$ Thus, the correct answer is C .