I've noticed that how people feel about this changes depending on how it is asked. If you take, for example, "better to let 5 guilty men go free than convict 1 innocent man", I think the "average" person is somewhat on the fence about that. And while this is just 1 example, this isn't total conjecture on my part. I was actually asked that exact question, with that exact ratio, by a defense attorney during jury selection. The majority of other potential jurors (honestly a bit to my horror) disagreed with that statement - they didn't think it was OK to let the 5 guilty go free even if it meant wrongly convicting an innocent person.
But if you instead ask people, "do you think it would be OK of nearly 17% of people in jail were actually innocent", the vast majority of people (or, at least all of the few people I asked that question to after my jury selection experience) think "no, that would mean there is a big problem with the criminal justice system".
People are bad at statistics.