Point p(5, 5); // ..or
Creates an automatic variable "on the stack". This means that it's lifetime and memory is fixed to it's scope.
Point* p = new Point(5, 5);
Creates a memory leak, double delete, or heap corruption in your program. This means that it almost certainly will crash your program, cause it to corrupt user data, or other fun side effects. Which is why actual C++ programmers use alternatives, such as...
auto p = make_unique<Point>(5, 5);
Creates a Point "on the heap". In this case, it's lifetime and memory is fixed to the lifetime of the owning
unique_ptr<Point>. This ownership can be transferred by move semantics. Unfortunately,
make_unique is not provided as Standard (a known defect) but it's relatively easy to roll your own. It is a simple factory function.
auto p = std::make_shared<Point>(5, 5);
Also creates a Point "on the heap". In this case, it's lifetime and memory is fixed to the lifetime of each
shared_ptr<Point> that points to it. When they are all destroyed, the
Point will be cleaned up.
shared_ptr<Point> can be copied, unlike
unique_ptr<Point>. This is very similar to Python's behaviour. However, do not forget that unlike in Python, there will be no machinery to break reference cycles.