df['MA'] = df.rolling(window=5).mean()

print(df)
#             Value    MA
# Date                   
# 1989-01-02   6.11   NaN
# 1989-01-03   6.08   NaN
# 1989-01-04   6.11   NaN
# 1989-01-05   6.15   NaN
# 1989-01-09   6.25  6.14
# 1989-01-10   6.24  6.17
# 1989-01-11   6.26  6.20
# 1989-01-12   6.23  6.23
# 1989-01-13   6.28  6.25
# 1989-01-16   6.31  6.27