5A is not TOO huge - that's like one std H4 headlight bulb
The other aspect of horn is that is only for very momentary use, not a constant load - short burst.
So that circuit is only pulling that for a few seconds.
With that in mind the OEM wiring will probably be 'adequate'
However - you will certainly be dropping voltage across the wiring and end up with significantly lower voltage at the horn itself (when it's operating that is)
That means it will not be so loud as if it were connected using a relay. (This may not be of concern to many as will still be considerably louder than the OEM - but not living up to its full potential)
The main point of concern is not so much the wiring itself - it's the switch; recognize you are going to be pulling that whole 5A through the switch - that is going to lead to pitting from the arcing as it makes/breaks and will eventually be a point of failure. Again, this can be somewhat mooted by the relatively infrequent use of the horn, so it may never become much of a concern.
Those are the pros and cons
Personally I would fit a relay, but you wouldn't be doing anything too risky using the OEM, but recognize the caveats stated