A softfork with post-quantum signature schemes might be proposed and applied first, but if the assumed damage of the quantum computation is enough to considered as a threat, a hardfork is higher chance. But the timeline? It won't happen in 5 year, probably 10 years before this quantum computers are built, usually these kind of computers are built for different purposes not to disrupt the whole internet since it will be affected as well lmao
As explained, Hardfork comes first and softfork-only is economic dead end.
The only threat is other chains being quantum safe soon as Bitcoin stucked in consensus besides would be loosing ranking.
Until it Hardforks to safety.
Are you sure you guys understand Bitcoin?