To solve this problem, we need to determine the energy levels for the 1-D harmonic oscillator. The energy levels for a 1-D harmonic oscillator are given by the equation:

E_n = (n + 1/2) * h * ω

Where E_n is the energy of the nth level, n is the quantum number of the level, h is the Planck's constant, and ω is the angular frequency of the oscillator.

In this case, we have 8 non-interacting spin -5/2 particles, which means we have 8 identical particles with a spin quantum number of -5/2. Since these particles are non-interacting, we can treat them as independent particles and determine the energy levels for each particle separately.

The spin quantum number of -5/2 corresponds to 6 possible spin states: -5/2, -3/2, -1/2, 1/2, 3/2, and 5/2. Each of these spin states has a degeneracy of 1, meaning there is only one way to assign each particle to a spin state.

To determine the energy levels for each particle, we can use the equation given above. However, we need to consider the degeneracy of each energy level. Since there are 6 possible spin states for each particle, each energy level will be 6-fold degenerate. Therefore, the energy levels for each particle are:

E_0 = (0 + 1/2) * h * ω = 1/2 * h * ω
E_1 = (1 + 1/2) * h * ω = 3/2 * h * ω
E_2 = (2 + 1/2) * h * ω = 5/2 * h * ω
E_3 = (3 + 1/2) * h * ω = 7/2 * h * ω
E_4 = (4 + 1/2) * h * ω = 9/2 * h * ω
E_5 = (5 + 1/2) * h * ω = 11/2 * h * ω
E_6 = (6 + 1/2) * h * ω = 13/2 * h * ω
E_7 = (7 + 1/2) * h * ω = 15/2 * h * ω

Since we have 8 identical particles, the total energy of the system will be the sum of the energies of each particle. Therefore, the first excited state energy for the system of 8 non-interacting spin -5/2 particles in the 1-D harmonic oscillator is:

E_total = 8 * E_1 = 8 * (3/2 * h * ω) = 12 * h * ω