Executing a c function in python code space

I have the following module written in C using Python C-api:

#include <Python.h>

static PyObject* init_factorial(PyObject* self, PyObject* args) {
    long long n;
    if (!PyArg_ParseTuple(args, "l", &n)) {
        return NULL;
    }

    if (n < 0) {
        PyErr_SetString(PyExc_ValueError, "Factorial is not defined for negative numbers");
        return NULL;
    }

    long result = 1;
    for (long i = 1; i <= n; ++i) {
        result *= i;
    }

    return PyLong_FromLong(result);
}

static PyMethodDef init_methods[] = {
    {"factorial", init_factorial, METH_VARARGS, "Calculates the factorial of a number"},
    {NULL, NULL, 0, NULL}
};

static struct PyModuleDef init_module = {
    PyModuleDef_HEAD_INIT,
    "init",
    "Module for calculating factorial",
    -1,
    init_methods
};


static int init_init_module(PyObject *module) {
    // some code ...
    PyRun_SimpleString("print(factorial(5))");

    return 0;
}

PyMODINIT_FUNC PyInit_init(void) {
    PyObject *m = PyModule_Create(&init_module);
    if (m == NULL)
        return NULL;

    // Call the function to print "factorial(5)" when importing
    if (init_init_module(m) < 0) {
        Py_DECREF(m);
        return NULL;
    }

    return m;
}

The program code is demo and non-working. How to modify the program code so that PyRun_SimpleString("print(factorial(5))"); printed the value of the factorial 5 to the console in the Python code space by calling the c-function factorial.

The code is executed immediately after importing the init module.