Yes, 5" seems at least an inch too long.

For example, Cannondale says no more than 55 mm of headset spacers (including the top bearing cap) under the stem, and most stems (that I have seen) are under 45 mm tall. That adds up to 4" at most. Most other manufacturers (that I have shopped) allow even less maximum headset spacer stack height. You should clarify with your fork manufacturer the maximum headset spacer stack height for that fork. An expander plug that extends past the bottom of the stem is highly recommended.