## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin B5' and 'milligrams of vitamin A'. Let's denote 'milligrams of vitamin B5' as $x_1$ and 'milligrams of vitamin A' as $x_2$. The objective function to maximize is $5x_1 + 7x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- Cognitive performance index: $13x_1 + 16x_2 \geq 10$
- Energy stability index: $4x_1 + 16x_2 \geq 27$
- Immune support index: $5x_1 + 5x_2 \geq 14$
- Digestive support index: $13x_1 + 8x_2 \geq 30$
- Muscle growth index: $2x_1 + 3x_2 \geq 19$
- Additional constraint: $10x_1 - 2x_2 \geq 0$
- Upper bounds:
  - Cognitive performance index: $13x_1 + 16x_2 \leq 33$
  - Energy stability index: $4x_1 + 16x_2 \leq 60$
  - Immune support index: $5x_1 + 5x_2 \leq 84$
  - Digestive support index: $13x_1 + 8x_2 \leq 87$
  - Muscle growth index: $2x_1 + 3x_2 \leq 53$

## 3: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B5'), ('x2', 'milligrams of vitamin A')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '13*x1 + 16*x2 >= 10',
        '4*x1 + 16*x2 >= 27',
        '5*x1 + 5*x2 >= 14',
        '13*x1 + 8*x2 >= 30',
        '2*x1 + 3*x2 >= 19',
        '10*x1 - 2*x2 >= 0',
        '13*x1 + 16*x2 <= 33',
        '4*x1 + 16*x2 <= 60',
        '5*x1 + 5*x2 <= 84',
        '13*x1 + 8*x2 <= 87',
        '2*x1 + 3*x2 <= 53'
    ]
}
```

## 4: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_vitamins():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="milligrams_of_vitamin_B5", lb=0)  # No lower bound specified, assuming 0
    x2 = model.addVar(name="milligrams_of_vitamin_A", lb=0)   # No lower bound specified, assuming 0

    # Objective function
    model.setObjective(5 * x1 + 7 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(13 * x1 + 16 * x2 >= 10)
    model.addConstr(4 * x1 + 16 * x2 >= 27)
    model.addConstr(5 * x1 + 5 * x2 >= 14)
    model.addConstr(13 * x1 + 8 * x2 >= 30)
    model.addConstr(2 * x1 + 3 * x2 >= 19)
    model.addConstr(10 * x1 - 2 * x2 >= 0)
    model.addConstr(13 * x1 + 16 * x2 <= 33)
    model.addConstr(4 * x1 + 16 * x2 <= 60)
    model.addConstr(5 * x1 + 5 * x2 <= 84)
    model.addConstr(13 * x1 + 8 * x2 <= 87)
    model.addConstr(2 * x1 + 3 * x2 <= 53)

    # Optimize
    model.optimize()

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

optimize_vitamins()
```