## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = number of books
- $x_2$ = number of magazines

The objective is to maximize profit. The profit per book is $5, and the profit per magazine is $8. So, the objective function can be represented as:

Maximize: $5x_1 + 8x_2$

The constraints are:
- Each book takes 10 minutes for printing, and each magazine takes 20 minutes for printing. The company has 5000 minutes available for printing:
  $10x_1 + 20x_2 \leq 5000$
- Each book takes 5 minutes for binding, and each magazine takes 3 minutes for binding. The company has 2000 minutes available for binding:
  $5x_1 + 3x_2 \leq 2000$
- The number of books and magazines cannot be negative:
  $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'books'), ('x2', 'magazines')],
    'objective_function': '5*x1 + 8*x2',
    'constraints': [
        '10*x1 + 20*x2 <= 5000',
        '5*x1 + 3*x2 <= 2000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='books', lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name='magazines', lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(5 * x1 + 8 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x1 + 20 * x2 <= 5000, name='printing_time')
    model.addConstr(5 * x1 + 3 * x2 <= 2000, name='binding_time')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: books = {x1.varValue}, magazines = {x2.varValue}")
        print(f"Max profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_printing_problem()
```