## Step 1: Define the symbolic representation of the problem
Let's denote the number of regular tickets as $x_1$ and the number of premium tickets as $x_2$. The objective is to maximize profit, which can be represented as $50x_1 + 100x_2$. The constraints based on the problem description are:
- $x_1 + x_2 \leq 1000$ (the amusement park can sell at most 1000 tickets)
- $x_2 \geq 100$ (the park reserves at least 100 tickets to be premium)
- $x_1 \geq 5x_2$ (at least 5 times as many people prefer to buy regular tickets than premium tickets)
- $x_1, x_2 \geq 0$ (non-negativity constraints, as the number of tickets cannot be negative)

## 2: Express the problem in the required symbolic format
The symbolic variables are:
- $x_1$ for regular tickets
- $x_2$ for premium tickets

The objective function is: $50x_1 + 100x_2$

The constraints are:
- $x_1 + x_2 \leq 1000$
- $x_2 \geq 100$
- $x_1 - 5x_2 \geq 0$
- $x_1, x_2 \geq 0$

In the required format:
```json
{
'sym_variables': [('x1', 'regular tickets'), ('x2', 'premium tickets')],
'objective_function': '50*x1 + 100*x2',
'constraints': ['x1 + x2 <= 1000', 'x2 >= 100', 'x1 - 5*x2 >= 0', 'x1 >= 0', 'x2 >= 0']
}
```

## 3: Translate the problem into Gurobi code
To solve this problem using Gurobi in Python, we will use the following code:

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="regular_tickets", lb=0, vtype=gurobi.GRB.INTEGER)  # Number of regular tickets
    x2 = model.addVar(name="premium_tickets", lb=0, vtype=gurobi.GRB.INTEGER)  # Number of premium tickets

    # Objective function: Maximize 50*x1 + 100*x2
    model.setObjective(50*x1 + 100*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 1000, name="total_tickets")  # At most 1000 tickets
    model.addConstr(x2 >= 100, name="min_premium_tickets")  # At least 100 premium tickets
    model.addConstr(x1 >= 5*x2, name="regular_to_premium_ratio")  # At least 5 times as many regular tickets as premium tickets

    # Solve the model
    model.optimize()

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

solve_amusement_park_ticket_problem()
```