How many chiral centers does estrogen have?

Contrary to what you might think, estrogen is a type of compound, and sometimes is confused to be a specific compound. There is estradiol, estriol, and estrone, for example. I will take a look at 17#\mathbf(beta)#-estradiol.

The only chiral centers there can be are those that are #sp^3# carbons. I'll redraw this with highlighted carbons:

Let's call carbon 1 the bottom left highlighted one, and trace the carbons, ending at the one on the upper right as carbon 5.

CARBON 1:
Substituents = hydride, #sp^2# aromatic carbon, #sp^2# methylene carbon, and isopropyl carbon
Priorities (1, 2, 3, 4): #sp^2# aromatic carbon, isopropyl carbon, #sp^2# methylene carbon, hydride
Stereochemical Label: S

CARBON 2:
Substituents = hydride, #sp^2# methylene carbon, isopropyl carbon A (carbon 3, further extended out to connect to another isopropyl carbon and an #sp^2# methylene carbon), and isopropyl carbon B (carbon 1, further extended out to connect to an #sp^2# methylene carbon and the #sp^2# aromatic carbon)
Priorities (1, 2, 3, 4): isopropyl carbon B, isopropyl carbon A, #sp^2# methylene carbon, hydride
Stereochemical Label: The reverse of S, which is R (due to the forward hydride, rather than in the rear)

CARBON 3:
Substituents = hydride, tert-butyl carbon, #sp^2# methylene carbon, and isopropyl carbon
Priorities (1, 2, 3, 4): tert-butyl carbon, isopropyl carbon, #sp^2# methylene carbon, hydride
Stereochemical Label: S

CARBON 4:
Substituents = methyl, #sp^2# methylene carbon, isopropyl carbon, and secondary alcohol
Priorities (1, 2, 3, 4): secondary alcohol, isopropyl carbon, #sp^2# methylene carbon, methyl
Stereochemical Label: The reverse of R, which is S (due to the forward methyl, rather than in the rear)

CARBON 5:
Substituents = hydroxide, #sp^2# methylene carbon, tert-butyl carbon, hydride
Priorities (1, 2, 3, 4): hydroxide, tert-butyl carbon, #sp^2# methylene carbon, hydride
Stereochemical Label: S