To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's denote:
- \(x_1\) as the number of vehicle tickets sold,
- \(x_2\) as the number of passenger tickets sold.

The objective is to maximize profit, given that each vehicle ticket and each passenger ticket yields a $50 profit. Thus, the objective function can be written as:
\[ \text{Maximize: } 50x_1 + 50x_2 \]

The constraints based on the problem description are:
1. The ferry can sell at most 100 tickets in total: \( x_1 + x_2 \leq 100 \)
2. At least 10 tickets must be reserved for vehicles: \( x_1 \geq 10 \)
3. At least 5 times as many people buy passenger tickets as vehicle tickets: \( x_2 \geq 5x_1 \)

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of vehicle tickets'), ('x2', 'number of passenger tickets')],
    'objective_function': '50*x1 + 50*x2',
    'constraints': ['x1 + x2 <= 100', 'x1 >= 10', 'x2 >= 5*x1']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="vehicle_tickets", vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name="passenger_tickets", vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(50*x1 + 50*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, name="total_tickets")
m.addConstr(x1 >= 10, name="min_vehicle_tickets")
m.addConstr(x2 >= 5*x1, name="passenger_to_vehicle_ratio")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: {x1.varName} = {int(x1.x)} tickets, {x2.varName} = {int(x2.x)} tickets")
else:
    print("No optimal solution found")

```