You don't need the standard to be qualified. There are 42 people who will be in the olympics for 5,000 meters. Only 24 of the slots at the moment are possible to be filled by people with the auto-standard. So 18 or more people will make it in on ranking in the world.
The US women who are currently ranked high enough, thus being qualified if the US sends them by being in our top 3, are:
Natosha Rogers, Whittni Morgan, Allie Buchalski, Parker Valby, Abby Nichols, Emily Infeld, Kayley Delay. And a few others would slide into ranking position with a top 3 at the US championships as long as it's a reasonably fast time around 15 flat.
I don't know why people still think the only way you can qualify is by getting the auto standard. There have been so many examples of people qualifying without the standard.
So the race isn't just out of the handful of people with the auto who aren't injured, any of these several additional runners would also be qualified via ranking.