Keep in mind that the 5 days are an absolute minimum, 10-14 days being the norm, so that contact could have been 14 days ago (or even longer - although that's rare).
POTUS himself is shielded extremely well. Yes he did those tarmac rallies, but keep in mind the skewed optics you get on TV. It's not like he was anywhere close to "common" (untested) people at all. And those around him (his staff) or the ones he came close to in the WH were all tested.
In your scenario it would be much more likely that someone close to him (such as Hope) caught it from an outsider and passed it on.