Laplace transform on simple low pass filter in Python
You're trying to plot in the time domain (ie. the x-axis is in seconds) but your formula is in the frequency domain (s is a complex frequency variable). You would need to perform the inverse Laplace transform to get back to the time domain.

This cannot be done unless you have a s-domain expression for Vin, which is tricky given that you just created it with random time domain values. Generally when doing this sort of s-domain stuff the output is only calculated for very simple (but very useful) inputs like step functions, impulses or single frequency sine waves.

There are many ways to go about what you're doing, and many of them require years of study. As suggested by @sstobbe, I think time domain simulation is probably your best route. Fortunately Python (via the SciPy library) has an equivalent lsim function. You just have to construct a system transfer function using lti. Something like this:

import matplotlib.pyplot as plt
from scipy import signal

sys = signal.lti(1,[1*0.1E-6,1])
t = np.linspace(0, 5, 150)
v_in = np.random.uniform(-0.005,0.005,150)+5
tout, y, x = signal.lsim(sys, v_in, t)

plt.plot(t, y)