This paper presents the current control design procedure of a single-phase grid-tied five-level packed U-cell inverter (PUC5) with an LCL output filter. The PUC5 inverter is used as an interface of renewable energy sources, such as solar applications. The LCL filter is calculated according to the grid-tied operation and converter ratings. An optimal controller, based on a linear quadratic regulator with integral action, is designed to inject a sinusoidal current with low harmonic distortion at unity power factor. For that design, the PUC5 inverter is modelled in the D-Q frame. The sensorless voltage control is incorporated into the switching technique to balance the PUC5 capacitor voltage and generate a five-level waveform at the output. Experimental tests are performed on a laboratory benchmark to confirm the theoretical design. The results prove the efficiency and accuracy of the adopted control strategy in a steady state and under transients of grid current, grid inductance, ac and dc voltage amplitudes.