To solve this optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the given objective function and constraints.

The objective function to minimize is: $1.66 \times (\text{milligrams of vitamin A})^2 + 2.23 \times (\text{milligrams of vitamin B5})^2 + 5.28 \times (\text{milligrams of vitamin B5})$.

Constraints are as follows:
- The immune support index from milligrams of vitamin A is 20.
- The cardiovascular support index from milligrams of vitamin A is 13.
- The immune support index for milligrams of vitamin B5 is 1.
- The cardiovascular support index from milligrams of vitamin B5 is 5.
- Total combined immune support index should be at least 32.
- Total combined cardiovascular support index should be at least 11.
- $5 \times (\text{milligrams of vitamin A})^2 - 4 \times (\text{milligrams of vitamin B5})^2 \geq 0$.
- The total combined immune support index should be no more than 54.
- The total combined cardiovascular support index should be no more than 43.
- Milligrams of vitamin A must be a whole number.
- Quantity of milligrams of vitamin B5 can be any real number.

Let's define our variables:
- $x_0$ = milligrams of vitamin A
- $x_1$ = milligrams of vitamin B5

Given the immune and cardiovascular support indices for each vitamin, we can directly calculate the contributions of $x_0$ and $x_1$ to these indices.

The total combined immune support index is $20x_0 + 1x_1 \geq 32$ and $\leq 54$.
The total combined cardiovascular support index is $13x_0 + 5x_1 \geq 11$ and $\leq 43$.

Here's how we can express this problem in Gurobi Python code:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_A")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B5")

# Objective function
m.setObjective(1.66 * x0**2 + 2.23 * x1**2 + 5.28 * x1, GRB.MINIMIZE)

# Constraints
m.addConstr(20*x0 + 1*x1 >= 32, name="immune_support_lower_bound")
m.addConstr(20*x0 + 1*x1 <= 54, name="immune_support_upper_bound")
m.addConstr(13*x0 + 5*x1 >= 11, name="cardiovascular_support_lower_bound")
m.addConstr(13*x0 + 5*x1 <= 43, name="cardiovascular_support_upper_bound")
m.addConstr(5*x0**2 - 4*x1**2 >= 0, name="vitamin_ratio_constraint")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin A: {x0.x}")
    print(f"Milligrams of Vitamin B5: {x1.x}")
else:
    print("No optimal solution found.")
```