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

Let's denote:
- \(x_1\) as the number of hardcover books.
- \(x_2\) as the number of paperback books.

The objective is to maximize profit, with a profit of $5 on each hardcover book and $2 on each paperback book. Thus, the objective function can be represented as:
\[ \text{Maximize:} \quad 5x_1 + 2x_2 \]

The constraints are as follows:
1. The total number of books displayed and sold cannot exceed 500.
\[ x_1 + x_2 \leq 500 \]
2. At least 50 books displayed must be hardcover.
\[ x_1 \geq 50 \]
3. At least 5 times as many readers prefer paperback books to hardcover books, implying the number of paperback books should be at least 5 times the number of hardcover books.
\[ x_2 \geq 5x_1 \]

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'number of hardcover books'), ('x2', 'number of paperback books')],
    'objective_function': '5*x1 + 2*x2',
    'constraints': ['x1 + x2 <= 500', 'x1 >= 50', 'x2 >= 5*x1']
}
```

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

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(name='hardcover_books', vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name='paperback_books', vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(5*x1 + 2*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 500, name='total_books')
m.addConstr(x1 >= 50, name='min_hardcover')
m.addConstr(x2 >= 5*x1, name='paperback_preference')

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of hardcover books: {x1.x}")
    print(f"Number of paperback books: {x2.x}")
    print(f"Maximum profit: ${5*x1.x + 2*x2.x:.2f}")
else:
    print("No optimal solution found.")
```