Interest rate targeting uses an unemployment buffer to keep wages and therefore prices under control. Poverty for those in work is entirely part of the plan. To fix the poverty problem you need to fix the structural viewpoint and return to the Beveridge condition - everybody must have an alternative living wage job offer available to them so that job competition works properly in favour of people. There must always be more jobs available than people that want them, not slightly fewer.
But that then runs into what Kalecki called "The Political Aspects of Full Employment" - a recommended read if you haven't already: https://mronline.org/2010/05/22/political-aspects-of-full-em...
Truly a 'wicked problem' - tied up with the concept of power
Even at 5% unemployment, your condition can be satisfied. For example, jobs might be unfilled because the candidates are unwilling to move. The candidates might be unqualified... shall we hire a random person as a brain surgeon? There could be a dozen job openings per person, and still the unemployment rate remains above zero.
As you move toward 0% unemployment, you push harder and harder against the problem of unsuitable workers. Reaching 0% is a bit like traveling at the speed of light: it is an unreachable goal, with difficulty rising dramatically as you get close.
This may differ by country, but you typically only show up in the numbers if you were fired. After all, if you quit your job, you aren't involuntarily unemployed, which is what the numbers are supposed to measure.
How often do people get fired? I remember reading numbers of every 20 years on average (don't have the source handy, I'm afraid), but let's call it every 10 years to make it conservative.
In a situation of true full employment, with a plethora of employers looking for employees, at least low to medium skill workers should be able to find a new job basically immediately -- within a week perhaps. Let's be conservative again and call it two months.
This means people are unemployed for two months every 10 years on average, which translates to ~1.7% frictional unemployment. That's way less than the 5% number you cite.
In fact, several industrialized nations saw unemployment rates below 1% for some time between the Second World War and the 1970s. In other words, achieving well below 2% unemployment rate is absolutely realistic.
If you convert the delta to the 5% number you cite to the US workforce, you get about 5 million people. 5 million people who are suffering simply due to political ideology.
On a more political level, I think it's important to keep in mind that the current situation (where people misleadingly talk about full employment even for unemployment rates much higher than 2%) is very beneficial to employers, because it greatly strengthens their bargaining position. Now add the fact that the majority of funding for economics think tanks is aligned with employer interests, and it's clear why the public discourse may be somewhat skewed and biased towards accepting inhumanely high rates of unemployment.