Combine multiple columns of data into one column

Hi,
I'm looking for a way to combine (not concatenate) the data from 5 columns in a single column. In other words, if I had 5 rows of data in column A, 3 rows of data in column B, 11 rows of data in column C, 8 rows of data in column D and 9 rows of data in column E, I want column F to have the 36 values (5+3+11+8+9 = 36) from the other columns.

The data has significantly more rows than I've used in my example and cutting and pasting is getting a little tedious every time I need to combine the data.

The data starts in row 3 for each column and any given row has no more than 258 values.
There are no intermingling blank cells in a given column; the blanks are at the end of each column.
The data is text, not numeric

(Back story: The data in columns A-E is generated using array formulas that pulls data from other worksheets. I need to combine those columns in to one, then remove duplicate values and sort the resulting combined column. The removing duplicates and sorting part I can handle; it's the combining part I'm having problems with. I was about to drop into VBA to solve this but since when it comes to writing formulas I'm a noob, I thought that I check here first. I saw this thread but no one solved it.)

Any help would greatly appreciated!
Thanks!
Paul