To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints using these variables.

Let's define:
- $x_1$ as the number of short words spelled,
- $x_2$ as the number of long words spelled.

The objective is to maximize the total points earned, which can be represented by the objective function: $3x_1 + 6x_2$.

The constraints based on the problem description are:
1. Spell at least 5 short words: $x_1 \geq 5$
2. Spell at least 2 long words: $x_2 \geq 2$
3. Spell at most 10 short words: $x_1 \leq 10$
4. Spell at most 5 long words: $x_2 \leq 5$
5. Spell at most 10 words in total: $x_1 + x_2 \leq 10$

All variables are non-negative since they represent counts of words.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of short words'), ('x2', 'number of long words')],
    'objective_function': '3*x1 + 6*x2',
    'constraints': ['x1 >= 5', 'x2 >= 2', 'x1 <= 10', 'x2 <= 5', 'x1 + x2 <= 10']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="short_words")
x2 = m.addVar(vtype=GRB.INTEGER, name="long_words")

# Set the objective function
m.setObjective(3*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 >= 5, "at_least_5_short")
m.addConstr(x2 >= 2, "at_least_2_long")
m.addConstr(x1 <= 10, "at_most_10_short")
m.addConstr(x2 <= 5, "at_most_5_long")
m.addConstr(x1 + x2 <= 10, "total_at_most_10")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Short words: {x1.x}")
    print(f"Long words: {x2.x}")
    print(f"Total points: {3*x1.x + 6*x2.x}")
else:
    print("No optimal solution found")
```