#Copyright RomanAILabs - Daniel Harding 2025
```python
import numpy as np
from scipy.linalg import solve

class FiveDSpacetimeEngine:
    def __init__(self, metric_tensor):
        self.metric_tensor = metric_tensor

    def spatial_metric(self, point):
        return self.metric_tensor[:, :3, :3].dot(point) + np.transpose(point).dot(self.metric_tensor[:, :3, :3])

    def spatial_distance(self, point1, point2):
        """Calculate the spatial distance between two points."""
        spatial_part = self.spatial_metric(point1 - point2)
        return np.sqrt(np.trace(spatial_part))

    def time_derivative(self, point, tangent_vector):
        """Calculate the time derivative of a tangent vector in 5D spacetime."""
        spatial_part = self.spatial_metric(point)
        time_derivative = tangent_vector[3]
        return np.array([spatial_part[:, i] for i in range(4)]) + time_derivative

    def geodesic_equation(self, point, tangent_vector):
        """Solve for the geodesic equation."""
        spatial_part = self.spatial_metric(point)
        tangent_vector = np.array(tangent_vector)

        # Derivative of the tangent vector
        tangent_derivative = self.time_derivative(point, tangent_vector)

        # Solve for the geodesic using the metric and the derivative of the tangent vector
        A = np.zeros((5, 5))
        b = np.zeros(5)
        for i in range(4):
            A[3, 3] += 1  # Time derivative of the tangent vector
            A[i, 4] = tangent_derivative[i]
            b[i] = tangent_derivative[i]
        
        # Solve the system of equations
        tangent_derivative = solve(A, b)

        # Update the tangent vector
        tangent_vector[3] += tangent_derivative[3]
        for i in range(4):
            tangent_vector[i] += tangent_derivative[i]

        return tangent_vector

    def geodesic(self, initial_point, initial_tangent_vector, time_interval, dt):
        """Calculate the geodesic of a point over a given time interval."""
        point = initial_point
        tangent_vector = initial_tangent_vector
        geodesic_points = [point]
        geodesic_tangent_vectors = [tangent_vector]

        for _ in range(int(time_interval / dt)):
            point, tangent_vector = self.geodesic_equation(point, tangent_vector)
            geodesic_points.append(point)
            geodesic_tangent_vectors.append(tangent_vector)

        return geodesic_points, geodesic_tangent_vectors

if __name__ == "__main__":
    # Example metric tensor for a 5D spacetime
    metric_tensor = np.array([
        [1, 0, 0, 0, 0],
        [0, 1, 0, 0, 0],
        [0, 0, 1, 0, 0],
        [0, 0, 0, 1, 0],
        [0, 0, 0, 0, 1]
    ])

    engine = FiveDSpacetimeEngine(metric_tensor)
    initial_point = np.array([1, 0, 0, 0, 0])
    initial_tangent_vector = np.array([0, 0, 0, 1, 0])
    time_interval = 100
    dt = 0.1

    geodesic_points, geodesic_tangent_vectors = engine.geodesic(initial_point, initial_tangent_vector, time_interval, dt)

    for point, tangent_vector in zip(geodesic_points, geodesic_tangent_vectors):
        print("Point:", point)
        print("Tangent Vector:", tangent_vector)
        print("\n")
```