We are given that five consecutive integers add up to $-5$. We are asked to find the greatest of these five integers.

1. Problem Description

We are given that five consecutive integers add up to $-5$. We are asked to find the greatest of these five integers.

2. Solution Steps

Let the five consecutive integers be $x, x+1, x+2, x+3,$ and $x+4$. Their sum is given as $-5$.

So, we can write the equation:

$x + (x+1) + (x+2) + (x+3) + (x+4) = -5$

Combining the terms, we get:

$5x + 10 = -5$

Subtracting 10 from both sides, we have:

$5x = -5 - 10$

$5x = -15$

Dividing both sides by 5, we get:

$x = -3$

So, the five consecutive integers are:

$x = -3$

$x+1 = -3 + 1 = -2$

$x+2 = -3 + 2 = -1$

$x+3 = -3 + 3 = 0$

$x+4 = -3 + 4 = 1$

The integers are $-3, -2, -1, 0, 1$. The greatest of these integers is $1$.

3. Final Answer

1