To tackle the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in algebraic terms.

Let's denote:
- $x_1$ as the milligrams of iron,
- $x_2$ as the milligrams of vitamin B5.

The objective function aims to minimize: $4.24x_1 + 9.4x_2$.

Given constraints are:
1. Kidney support index for iron: $5x_1$
2. Immune support index for iron: $6x_1$
3. Kidney support index for vitamin B5: $13x_2$
4. Immune support index for vitamin B5: $4x_2$
5. Total kidney support index minimum: $5x_1 + 13x_2 \geq 22$
6. Same as constraint 5, emphasizing the total should be at least 22.
7. Total immune support index minimum: $6x_1 + 4x_2 \geq 15$
8. Same as constraint 7.
9. Linear combination of iron and vitamin B5: $6x_1 - 3x_2 \geq 0$
10. Total kidney support index maximum: $5x_1 + 13x_2 \leq 45$
11. Total immune support index maximum: $6x_1 + 4x_2 \leq 29$

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'milligrams of iron'), ('x2', 'milligrams of vitamin B5')],
    'objective_function': '4.24*x1 + 9.4*x2',
    'constraints': [
        '5*x1 + 13*x2 >= 22',
        '6*x1 + 4*x2 >= 15',
        '6*x1 - 3*x2 >= 0',
        '5*x1 + 13*x2 <= 45',
        '6*x1 + 4*x2 <= 29'
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python. Note that we'll define $x_1$ as a continuous variable and $x_2$ as an integer variable based on the problem statement.

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_iron")
x2 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="milligrams_of_vitamin_B5")

# Define the objective function
m.setObjective(4.24*x1 + 9.4*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 13*x2 >= 22, "kidney_support_min")
m.addConstr(6*x1 + 4*x2 >= 15, "immune_support_min")
m.addConstr(6*x1 - 3*x2 >= 0, "linear_combination")
m.addConstr(5*x1 + 13*x2 <= 45, "kidney_support_max")
m.addConstr(6*x1 + 4*x2 <= 29, "immune_support_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of iron: {x1.x}")
    print(f"Milligrams of vitamin B5: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```