Calculate the sum of the infinite geometric series: 5 + (-2) + (4/5) + ...
To find the sum of an infinite geometric series, we can use the formula:

Sum = a / (1 - r)

where 'a' is the first term and 'r' is the common ratio between consecutive terms.

In this case, the first term (a) is 5, and the common ratio (r) can be found by dividing any term by its preceding term. For example, (-2) / 5 = -2/5.

So, the common ratio (r) is -2/5.

Now, we can plug these values into the formula:

Sum = 5 / (1 - (-2/5))
Sum = 5 / (1 + 2/5)
Sum = 5 / (7/5)
Sum = 5 * (5/7)
Sum = 25/7

Therefore, the sum of the infinite geometric series is 25/7.