Define a 2D Gaussian probability with five peaks
If I understand what you're asking, check out Gaussian Mixture Models and Expectation Maximization. I don't know of any pre-implemented versions of these in Python, although I haven't looked too hard.
I have a 2D data and it contains five peaks. Could I fit five 2D Gaussians function to obtain the peaks?  In my problem, the peaks do not refer to the clustering problem.  Which I think EM would be an appropriate answer for it. 
In my case I measure a variable in x-y space and it shows maximum in more than one position. Is still fitting Fourier series or using Expectation-Maximization method an applicable solution to my problem?
In order to make my likelihood, do I need to just add up the five 2D Gaussians distributions with x and y and the height of each peak as variables?