To solve these expressions, we can use the formula for the sum of a geometric series:

For the first expression:
1 + 1/2 + 1/4 + 1/8 + 1/16

The common ratio is 1/2, and the first term is 1. We can use the formula:

S = a(1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the values, we have:
S = 1(1 - (1/2)^5) / (1 - 1/2)
S = 1(1 - 1/32) / (1/2)
S = (32 - 1) / (1/2)
S = 31 / (1/2)
S = 31 * 2
S = 62

So, the sum of the first expression is 62.

For the second expression:
1 - 1/2 + 1/4 - 1/8 + 1/16

Again, the common ratio is 1/2, and the first term is 1. Using the same formula:

S = a(1 - r^n) / (1 - r)

Plugging in the values, we have:
S = 1(1 - (1/2)^5) / (1 - (-1/2))
S = 1(1 - 1/32) / (1 + 1/2)
S = (32 - 1) / (3/2)
S = 31 / (3/2)
S = 31 * (2/3)
S = 62/3

So, the sum of the second expression is 62/3.