Why is there a limit to 5 tags for questions?
Why is there no information for the user that there is a limit until they try enter more than 5 tags?
There's a limit to ensure that you think well about how your question should be tagged and don't resort to just tagging it with everything in hope that it will somehow surface to more people. It also keeps the tag system focused.
The limit is not surfaced until you enter 5 tags because you don't need to know the limit until you reach it.
Your question seems to imply you want it to work differently. What would you propose?
Over the years, five tags has proven to be sufficient for the vast, vast majority of questions without trying to overly-categorize questions from every conceivable context.
If you find that you consistently need more than five tags, there's a pretty good chance you are adding superfluous tags that aren't really needed. Over the years, five tags has shown to be a good limit because it encourages you to pare down the tags to just the essentials. Tagging is supposed to help categorize your question into its major areas of interest. It is not meant to try and sum up your question into every conceivable interest.
If we raised the limit beyond five, there will be authors that feel they need just one more tag, and one more tag, and one more tag. Oftentimes, if you need more than five tags, you may be asking questions whose scope is simply too large and encompasses too many areas of interest.
If you feel more tags are needed systemically, I would suggest linking to a selection questions you feel need more tags. Either you'll make your case stronger, or the folks here will be able to help you improve your tag selections.