That's not usually the advice financial counselors give. Dave Ramsey, for instance, would probably say keep $1k in the bank and pay pay off $9k of the debt and [snowball] the remaining payments.
Also, assuming you can get a 12% ROI over the years, and accounting for inflation, you'd be left with 12%-5%-4%=3%
Is that hypothetical 3% gain worth keeping the debt, which has risks of its own? e.g. you are incapacitated due to an accident, or you incur a huge medical bill that you need to split into payments, but you can't pay much because, oh "i just have this loan at 5% that's not worth paying off.