Follow these steps to implement the four- and five-factor models in Python.

1. Import the libraries:

import pandas as pd
import yfinance as yf
import statsmodels.formula.api as smf
import pandas_datareader.data as web

2. Specify the risky asset and the time horizon:

RISKY_ASSET = 'AMZN'
START_DATE = '2013-12-31'
END_DATE = '2018-12-31'

3. Download the risk factors from prof. French's website:

# three factors 
df_three_factor = web.DataReader('F-F_Research_Data_Factors', 
                                 'famafrench', start=START_DATE)[0]
df_three_factor.index = df_three_factor.index.format()

# momentum factor
df_mom = web.DataReader('F-F_Momentum_Factor', 'famafrench', 
                        start=START_DATE)[0]
df_mom.index = df_mom.index.format()

# five factors
df_five_factor = web.DataReader('F-F_Research_Data_5_Factors_2x3', 
                                'famafrench', 
                                start=START_DATE)[0]
df_five_factor.index = df_five_factor.index.format()

4. Download the data of the risky asset from Yahoo Finance:

asset_df = yf.download(RISKY_ASSET,
                       start=START_DATE,
                       end=END_DATE,
                       adjusted=True,
                       progress=False)

5. Calculate the monthly returns:

y = asset_df['Adj Close'].resample('M') 
                         .last() 
                         .pct_change() 
                         .dropna()

y.index = y.index.strftime('%Y-%m')
y.name = 'return'

6. Merge the datasets for the four-factor model:

# join all datasets on the index
four_factor_data = df_three_factor.join(df_mom).join(y)

# rename columns
four_factor_data.columns = ['mkt', 'smb', 'hml', 'rf', 'mom', 
                            'rtn']

# divide everything (except returns) by 100
four_factor_data.loc[:, four_factor_data.columns != 'rtn'] /= 100

# convert index to datetime
four_factor_data.index = pd.to_datetime(four_factor_data.index, 
                                        format='%Y-%m')

# select period of interest
four_factor_data = four_factor_data.loc[START_DATE:END_DATE]

# calculate excess returns
four_factor_data['excess_rtn'] = four_factor_data.rtn - four_factor_data.rf

7. Merge the datasets for the five-factor model:

# join all datasets on the index
five_factor_data = df_five_factor.join(y)

# rename columns
five_factor_data.columns = ['mkt', 'smb', 'hml', 'rmw', 'cma', 
                            'rf', 'rtn']

# divide everything (except returns) by 100
five_factor_data.loc[:, five_factor_data.columns != 'rtn'] /= 100

# convert index to datetime
five_factor_data.index = pd.to_datetime(five_factor_data.index, 
                                        format='%Y-%m')

# select period of interest
five_factor_data = five_factor_data.loc[START_DATE:END_DATE]

# calculate excess returns
five_factor_data['excess_rtn'] = five_factor_data.rtn - five_factor_data.rf

8. Estimate the four-factor model:

four_factor_model = smf.ols(formula='excess_rtn ~ mkt + smb + hml + 
                            mom', data=four_factor_data).fit()

print(four_factor_model.summary())

The following summary shows the results:

9. Estimate the five-factor model:

five_factor_model = smf.ols(
    formula='excess_rtn ~ mkt + smb + hml + rmw + cma', 
    data=five_factor_data
).fit()

print(five_factor_model.summary())

The following summary shows the results:

According to the five-factor model, Amazon's excess returns are negatively exposed to most of the factors (all but the market factor). Here, we present an example of the interpretation of the coefficients: an increase by 1 percentage point in the market factor results in an increase of 0.015 p.p. In other words, for a 1% return by the market factor, we can expect our portfolio (Amazon's stock) to return 1.5508 * 1% in excess of the risk-free rate.

Similarly to the three-factor model, if the five-factor model fully explains the excess stock returns, the estimated intercept should be statistically indistinguishable from zero (which is the case for the considered problem).