Well, leaving aside looking at current rates rather than leading indicators (since, while problematic, its a lot more convenient), the time you were referencing with a ~5% Fed funds rate also had inflation rates near 5%, not hovering around 1% (like now) after more than a year of being substantially below 1%.
> and yet raising them to 0.25% is considered shocking, even with inflation very low
The Fed raises rates to control inflation. With low inflation, you expect low rates. It also lowers rates to improve employment, but with virtually no inflation, there's little reason for tightening the money supply.
The last time inflation was this low this long -- in the mid 1950s -- the effective Fed Funds rate was also quite low, though a bit higher than now (around 1%, rather than 0.37% now).