The Variance is defined as:
The average of the squared differences from the Mean.
First, we need to calculate the mean. You could do it by hand, but it's fairly clear that it's 3. (If not, add up the numbers and divide by 5).
Now, we have to calculate the variance. This is the sum of the square of the differences of each piece of the data and the mean. Hard to say in words!
The mean is 3, so we have:
(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^...
We then divide by the number of values, which is 5, giving us 2.
The standard deviation is simply the square root of this value:
\sqrt(2)=1.414 (about)
We should not take the sample standard deviation here (which would divide by 4 instead), because it the data is just a set of numbers, not data from a random variable.
