To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of pancakes to be made
- $x_2$ as the number of waffles to be made

The objective function is to maximize profit. Given that each pancake generates $5 and each waffle generates $7, we have the objective function as:
\[ \text{Maximize: } 5x_1 + 7x_2 \]

For the constraints:

- Each pancake requires 30 grams of flour, and each waffle requires 50 grams of flour. The diner has available 5000 grams of flour. So, we have:
\[ 30x_1 + 50x_2 \leq 5000 \]
- Each pancake requires 10 grams of butter, and each waffle requires 15 grams of butter. The diner has available 2000 grams of butter. So, we have:
\[ 10x_1 + 15x_2 \leq 2000 \]
- Additionally, $x_1$ and $x_2$ must be non-negative since they represent the number of items to be made.

In symbolic representation with natural language objects:

```json
{
    'sym_variables': [('x1', 'pancakes'), ('x2', 'waffles')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '30*x1 + 50*x2 <= 5000',
        '10*x1 + 15*x2 <= 2000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

# Create a new model
model = Model("Breakfast_Diner")

# Define variables
x1 = model.addVar(vtype=GRB.CONTINUOUS, name="pancakes")
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="waffles")

# Set the objective function
model.setObjective(5*x1 + 7*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(30*x1 + 50*x2 <= 5000, "flour_limit")
model.addConstr(10*x1 + 15*x2 <= 2000, "butter_limit")

# Solve the model
model.optimize()

# Print solution
if model.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found")
```