The current experimental uncertainty on the CKM unitarity triangle angle $\phi_3$ is significantly larger than that on the standard model prediction. A more precise measurement of $\phi_3$ is crucial for testing the SM description of $CP$ violation and probing for new physics effects. The precision can be improved by exploring new $B$ and $D$ decay modes. The first model-independent measurement of the CKM angle $\phi_3$ using $B^{\pm} \to D(K_{\rm S}^0 \pi^+ \pi^- \pi^0) K^{\pm}$ decays is presented here. The GGSZ method is used by binning the five-dimensional phase space of the $D$ decay. This analysis uses the measurement of the average strong-phase differences across the phase space in $D\to K_{\rm S}^0 \pi^+ \pi^- \pi^0$ decays from CLEO-c, as input. The results are obtained from the full Belle data set with an integrated luminosity of 711 fb$^{-1}$ collected at the $\Upsilon(4S)$ resonance.