We present new Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the [CII] 158 $mu$m transition and the dust continuum in HZ4, a typical star-forming galaxy when the Universe was only $sim1$ Gyr old ($zapprox5.5$). Our high $approx0.3$ spatial resolution allow us to study the relationships between [CII] line emission, star formation rate (SFR), and far-infrared (FIR) emission on spatial scales of $sim2$ kpc. In the central $sim$4 kpc of HZ4, the [CII]/FIR ratio is $sim3times10^{-3}$ on global scales as well as on spatially-resolved scales of $sim$2 kpc, comparable to the ratio observed in local moderate starburst galaxies such as M82 or M83. For the first time in an individual normal galaxy at this redshift, we find evidence for outflowing gas from the central star-forming region in the direction of the minor-axis of the galaxy. The projected velocity of the outflow is $sim400$ km s$^{-1}$, and the neutral gas mass outflow rate is $sim3-6$ times higher than the SFR in the central region. Finally, we detect a diffuse component of [CII] emission, or [CII]-halo, that extends beyond the star-forming disk and has a size of $sim12$ kpc in diameter. Most likely the outflow, which has a velocity approximately half the escape velocity of the system, is in part responsible for fueling the [CII] extended emission. Together with the kinematic analysis of HZ4 (presented in a forthcoming paper), the analysis supports that HZ4 is a typical star-forming disk at $zsim5$ with interstellar medium (ISM) conditions similar to present-day galaxies forming stars at a similar level, driving a galactic outflow that may already play a role in its evolution.