## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of potassium' and 'milligrams of vitamin B5', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $2.82x_1 + 7.0x_2$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. The digestive support index for $x_1$ is 6, and for $x_2$ is 13.
2. $6x_1 + 13x_2 \geq 82$
3. $-5x_1 + x_2 \geq 0$
4. $6x_1 + 13x_2 \leq 164$

## 4: Determine the bounds of the variables
Given that there can be a non-integer number of milligrams of potassium and a fractional amount of milligrams of vitamin B5, $x_1$ and $x_2$ are not restricted to integer values.

## 5: Express the problem in a JSON format for clarity
```json
{
'sym_variables': [('x1', 'milligrams of potassium'), ('x2', 'milligrams of vitamin B5')],
'objective_function': '2.82*x1 + 7.0*x2',
'constraints': [
    '6*x1 + 13*x2 >= 82',
    '-5*x1 + x2 >= 0',
    '6*x1 + 13*x2 <= 164'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="milligrams_of_potassium", lb=0)  # Assuming lower bound is 0
    x2 = model.addVar(name="milligrams_of_vitamin_B5", lb=0)  # Assuming lower bound is 0

    # Objective function
    model.setObjective(2.82 * x1 + 7.0 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(6 * x1 + 13 * x2 >= 82, name="digestive_support_index_min")
    model.addConstr(-5 * x1 + x2 >= 0, name="vitamin_constraint")
    model.addConstr(6 * x1 + 13 * x2 <= 164, name="digestive_support_index_max")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```