case_when function from R to Python

You want to use np.select:

conditions = [
    (df["age"].lt(10)),
    (df["age"].ge(10) & df["age"].lt(20)),
    (df["age"].ge(20) & df["age"].lt(30)),
    (df["age"].ge(30) & df["age"].lt(50)),
    (df["age"].ge(50)),
]
choices = ["baby", "kid", "young", "mature", "grandpa"]

df["elderly"] = np.select(conditions, choices)

# Results in:
#      name  age  preTestScore  postTestScore  elderly
#  0  Jason   42             4             25   mature
#  1  Molly   52            24             94  grandpa
#  2   Tina   36            31             57   mature
#  3   Jake   24             2             62    young
#  4    Amy   73             3             70  grandpa

The conditions and choices lists must be the same length.
There is also a default parameter that is used when all conditions evaluate to False.

np.select is great because it's a general way to assign values to elements in choicelist depending on conditions.

However, for the particular problem OP tries to solve, there is a succinct way to achieve the same with the pandas' cut method.

bin_cond = [-np.inf, 10, 20, 30, 50, np.inf]            # think of them as bin edges
bin_lab = ["baby", "kid", "young", "mature", "grandpa"] # the length needs to be len(bin_cond) - 1
df["elderly2"] = pd.cut(df["age"], bins=bin_cond, labels=bin_lab)

#     name  age  preTestScore  postTestScore  elderly elderly2
# 0  Jason   42             4             25   mature   mature
# 1  Molly   52            24             94  grandpa  grandpa
# 2   Tina   36            31             57   mature   mature
# 3   Jake   24             2             62    young    young
# 4    Amy   73             3             70  grandpa  grandpa