Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion via singlet-triplet spin blockade, which can be detected in-situ using gate-based dispersive sensing. In systems with a complex energy spectrum, like silicon quantum dots, accurately identifying when singlet-triplet blockade occurs is hence of major importance for scalable qubit readout. In this work, we present a description of spin blockade physics in a tunnel-coupled silicon double quantum dot defined in the corners of a split-gate transistor. Using gate-based magnetospectroscopy, we report successive steps of spin blockade and spin blockade lifting involving spin states with total spin angular momentum up to $S=3$. More particularly, we report the formation of a hybridized spin quintet state and show triplet-quintet and quintet-septet spin blockade. This enables studies of the quintet relaxation dynamics from which we find $T_1 \sim 4 ~\mu s$. Finally, we develop a quantum capacitance model that can be applied generally to reconstruct the energy spectrum of a double quantum dot including the spin-dependent tunnel couplings and the energy splitting between different spin manifolds. Our results open for the possibility of using Si CMOS quantum dots as a tuneable platform for studying high-spin systems.