As likely as any other flu, which is basically guaranteed. I doubt it will become a 2020-style shutdown though, purely because that would be unpopular
It's not "basically guaranteed". H5N1 has been around for a while and was never really considered a serious threat before.
And a 2020-style shutdown would be the least of everyone's worries if this thing does blow up. The fatality rates in humans is around 40% or so. At that rate, you're talking about at the very least a complete breakdown of society as we know it, if not a full-blown extinction-level event.