Python: Summing every five rows of column b data and create a new column - python-3.x

Question

I have a dataframe like below. I would like to sum row 0 to 4 (every 5 rows) and create another column with summed value ("new column"). My real dataframe has 263 rows so, last three rows every 12 rows will be sum of three rows only. How I can do this using Pandas/Python. I have started to learn Python recently. Thanks for any advice in advance!
My data patterns is more complex as I am using the index as one of my column values and it repeats like:
Row Data "new column"
0 5
1 1
2 3
3 3
4 2 14
5 4
6 8
7 1
8 2
9 1 16
10 0
11 2
12 3 5
0 3
1 1
2 2
3 3
4 2 11
5 2
6 6
7 2
8 2
9 1 13
10 1
11 0
12 1 2
...
259 50 89
260 1
261 4
262 5 10
I tried iterrows and groupby but can't make it work so far.

Answer 1

Use this:
df['new col'] = df.groupby(df.index // 5)['Data'].transform('sum')[lambda x: ~(x.duplicated(keep='last'))]
Output:
Data new col
0 5 NaN
1 1 NaN
2 3 NaN
3 3 NaN
4 2 14.0
5 4 NaN
6 8 NaN
7 1 NaN
8 2 NaN
9 1 16.0
Edit to handle updated question:
g = df.groupby(df.Row).cumcount()
df['new col'] = df.groupby([g, df.Row // 5])['Data']\
.transform('sum')[lambda x: ~(x.duplicated(keep='last'))]
Output:
Row Data new col
0 0 5 NaN
1 1 1 NaN
2 2 3 NaN
3 3 3 NaN
4 4 2 14.0
5 5 4 NaN
6 6 8 NaN
7 7 1 NaN
8 8 2 NaN
9 9 1 16.0
10 10 0 NaN
11 11 2 NaN
12 12 3 5.0
13 0 3 NaN
14 1 1 NaN
15 2 2 NaN
16 3 3 NaN
17 4 2 11.0
18 5 2 NaN
19 6 6 NaN
20 7 2 NaN
21 8 2 NaN
22 9 1 13.0
23 10 1 NaN
24 11 0 NaN
25 12 1 2.0