What do you call an average that does not include outliers?

For example if you have a set:

{90,89,92,91,5} avg = 73.4


but excluding the outlier (5) we have

{90,89,92,91(,5)} avg = 90.5


How do you describe this average in statistics?

It's called the trimmed mean.  Basically what you do is compute the mean of the middle 80% of your data, ignoring the top and bottom 10%. Of course, these numbers can vary, but that's the general idea.