The ARGO-YBJ detector is an extensive air shower array that has been used to monitor the northern $\gamma$-ray sky at energies above 0.3 TeV from 2007 November to 2013 January. In this paper, we present the results of a sky survey in the declination band from $-10^{\circ}$ to $70^{\circ}$, using data recorded over the past five years. With an integrated sensitivity ranging from 0.24 to $\sim$1 Crab units depending on the declination, six sources have been detected with a statistical significance greater than 5 standard deviations. Several excesses are also reported as potential $\gamma$-ray emitters. The features of each source are presented and discussed. Additionally, $95\%$ confidence level upper limits of the flux from the investigated sky region are shown. Specific upper limits for 663 GeV $\gamma$-ray AGNs inside the ARGO-YBJ field of view are reported. The effect of the absorption of $\gamma$-rays due to the interaction with extragalactic background light is estimated.
