Group by consecutive values in one column and select the earliest and latest date for each group

This solution expects the dates to be sorted from the earliest to the latest, as in the provided example data.

from itertools import groupby
from io import StringIO

import pandas as pd


df = pd.read_csv(
    StringIO(
        """col1 col2    col3    col4    col5
a   2021-07-03  17:08   2021-07-04  10:41
b   2021-07-10  04:14   2021-07-11  04:32
c   2021-07-13  02:03   2021-07-14  00:45
d   2021-07-14  21:23   2021-07-15  02:59
d   2021-07-15  04:05   2021-07-15  09:41
e   2021-07-17  13:50   2021-07-18  08:49
a   2021-07-18  10:51   2021-07-18  12:27
a   2021-07-18  13:55   2021-07-19  06:26
f   2021-09-20  22:36   2021-09-20  23:19
f   2021-09-21  23:45   2021-09-23  10:12
"""
    ),
    delim_whitespace=True,
    header=0,
)

# Group by consecutive values in col1
groups = [list(group) for key, group in groupby(df["col1"].values.tolist())]
group_end_indices = pd.Series(len(g) for g in groups).cumsum()
group_start_indices = (group_end_indices - group_end_indices.diff(1)).fillna(0).astype(int)

filtered_df = []
for start_ix, end_ix in zip(group_start_indices, group_end_indices):
    group = df.iloc[start_ix:end_ix]
    if group.shape[0] > 1:
        group.iloc[0][["col4", "col5"]] = group.iloc[-1][["col4", "col5"]]
    filtered_df.append(group.iloc[0])
filtered_df = pd.DataFrame(filtered_df).reset_index(drop=True)
print(filtered_df)

Output:

  col1        col2   col3        col4   col5
0    a  2021-07-03  17:08  2021-07-04  10:41
1    b  2021-07-10  04:14  2021-07-11  04:32
2    c  2021-07-13  02:03  2021-07-14  00:45
3    d  2021-07-14  21:23  2021-07-15  09:41
4    e  2021-07-17  13:50  2021-07-18  08:49
5    a  2021-07-18  10:51  2021-07-19  06:26
6    f  2021-09-20  22:36  2021-09-23  10:12

You could use the fact that these are datetimes and use pandas groupby to select the earlier dates from col2+col3 and later dates from col4+col5 for each group.

filtered_df = (
    # convert each pair of columns to datetimes
    df.assign(c1 = pd.to_datetime(df['col2'] + ' ' + df['col3']), c2 = pd.to_datetime(df['col4'] + ' ' + df['col5']))
    # groupby consecutive col1 values and keep earliest c1 and latest c2 values
    .groupby(df['col1'].shift().ne(df['col1']).cumsum()).agg({'col1': 'first', 'c1': 'min', 'c2': 'max'})
    # split datetimes back into separate columns by dates and times
    .set_index('col1', append=True).astype(str).stack().str.split(expand=True).unstack()
    # rename columns
    .set_axis(['col2', 'col4', 'col3', 'col5'], axis=1).sort_index(axis=1)
    # bring col1 in as a column 
    .reset_index(level=1).reset_index(drop=True)
)
filtered_df