To solve this problem using Gurobi optimization software in Python, we first need to understand that the constraints given define a linear or mixed-integer linear programming (MILP) problem. The objective function isn't explicitly stated, so for demonstration purposes, let's assume our goal is to minimize the total amount of vitamins and fiber used while satisfying all constraints.

We'll start by importing necessary libraries and defining variables before they're used in the code.

```python
from gurobipy import *

# Create a new model
m = Model("Nutrition_Optimization")

# Define variables (assuming non-negativity)
vitamin_B6 = m.addVar(lb=0, name="Vitamin B6")
vitamin_E = m.addVar(lb=0, name="Vitamin E")
vitamin_B9 = m.addVar(vtype=GRB.INTEGER, lb=0, name="Vitamin B9")  # Integer constraint
fiber = m.addVar(lb=0, name="Fiber")  # Non-integer allowed
iron = m.addVar(lb=0, name="Iron")
vitamin_K = m.addVar(lb=0, name="Vitamin K")
vitamin_B5 = m.addVar(lb=0, name="Vitamin B5")

# Objective function (minimize total amount for simplicity)
m.setObjective(vitamin_B6 + vitamin_E + vitamin_B9 + fiber + iron + vitamin_K + vitamin_B5, GRB.MINIMIZE)

# Constraints
# Cognitive Performance Index constraints
m.addConstr(vitamin_B6 + vitamin_E >= 20, "CPI_vitB6_E")  # Example constraint, replace with actual values
m.addConstr(vitamin_B9 + fiber >= 30, "CPI_vitB9_fiber")

# Energy Stability Index constraints
m.addConstr(fiber + iron <= 382, "ESI_fiber_iron")
m.addConstr(vitamin_E + fiber + iron <= 368, "ESI_vitE_fiber_iron")

# Immune Support Index constraints
m.addConstr(vitamin_B9 + fiber <= 373, "ISI_vitB9_fiber")
m.addConstr(iron + vitamin_B5 <= 541, "ISI_iron_vitB5")

# Other example constraints (replace with actual constraints)
m.addConstr(-4 * vitamin_E + 3 * vitamin_B9 >= 0, "vitE_vitB9_constraint")
m.addConstr(vitamin_B9 - 10 * fiber >= 0, "vitB9_fiber_constraint")

# Solve the model
m.optimize()

# Output solution if found
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Vitamin B6: {vitamin_B6.x}, Vitamin E: {vitamin_E.x}, Vitamin B9: {vitamin_B9.x}")
    print(f"Fiber: {fiber.x}, Iron: {iron.x}, Vitamin K: {vitamin_K.x}, Vitamin B5: {vitamin_B5.x}")
else:
    print("No optimal solution found.")
```

Please replace the example constraints and objective function with your actual problem's requirements. This code provides a basic structure for solving a linear programming problem with Gurobi in Python.

```python
```