Not an astrophysicist, but I'm thinking 5 AU could quickly fry the Earth - because it takes very little in the way of solar comets, asteroids, and dust to build a temporary accretion disk around such a black hole. That disk might have a temperature of >1M degrees. Plus the dynamo effects of the disk's interactions with the solar magnetic field? Yeah. 5 ly sounds much safer.
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Yeah, I'm sure you're right. I was looking purely at orbital mechanics and gravity, but I think a four-stellar-mass black hole would certainly have other harmful environmental effects that would be felt at that range.
> Yeah. 5 ly sounds much safer.
Well yeah.
I clearly could've phrased this better though: I was aiming for "here is an example distance which *is* bad", not as it appears to have been understood "here is the distance where it is *not* bad".
I mostly noticed your "might have an unplesant climate impact by increasing the eccentricity of our orbit", and thought that'd be the least of Earth's worries.
Black hole gravity is ruthless about turning nearby mass into deadly fireworks.