## 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 and the objective function, and then list the constraints.

### Variables
- $x_1$: Number of slow balls hit
- $x_2$: Number of fast balls hit

### Objective Function
The objective is to maximize points, where each slow ball hit gives 3 points and each fast ball hit gives 5 points. Therefore, the objective function is:
\[ \text{Maximize:} \quad 3x_1 + 5x_2 \]

### Constraints
1. Hit at least 5 slow balls: $x_1 \geq 5$
2. Hit at least 3 fast balls: $x_2 \geq 3$
3. Hit at most 8 slow balls: $x_1 \leq 8$
4. Hit at most 8 fast balls: $x_2 \leq 8$
5. Hit no more than 12 balls in total: $x_1 + x_2 \leq 12$

## Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 'slow balls'), ('x2', 'fast balls')],
  'objective_function': '3*x1 + 5*x2',
  'constraints': [
    'x1 >= 5',
    'x2 >= 3',
    'x1 <= 8',
    'x2 <= 8',
    'x1 + x2 <= 12'
  ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, ub=8, name="slow_balls", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(lb=0, ub=8, name="fast_balls", vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 3*x1 + 5*x2
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 >= 5, name="min_slow_balls")
    model.addConstr(x2 >= 3, name="min_fast_balls")
    model.addConstr(x1 <= 8, name="max_slow_balls")
    model.addConstr(x2 <= 8, name="max_fast_balls")
    model.addConstr(x1 + x2 <= 12, name="total_balls")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: slow balls = {x1.varValue}, fast balls = {x2.varValue}")
    else:
        print("No optimal solution found.")

solve_problem()
```