您可以转换 datetime 列到 long 并在rangebetween（）函数中传入相当于5天的秒数。

from pyspark.sql.functions import *
from pyspark.sql import functions as F
from pyspark.sql.window import Window

df = df.withColumn("date_long", to_date(substring(col("datetime"),0,10), "yyyy-MM-dd"))\
        .withColumn("date_long", unix_timestamp('date_long', 'yyyy-MM-dd'))

days = lambda i: i * 86400 
w = (Window.partitionBy('cust_id').orderBy("date_long").rangeBetween(0,days(5)))

df.withColumn('5_day_visit', F.count("*").over(w)).drop('date_long').show()
+-------+----------------+-----------+                                          
|cust_id|        datetime|5_day_visit|
+-------+----------------+-----------+
|      1|2020-08-15 15:20|          4|
|      1|2020-08-15 16:20|          4|
|      1|2020-08-17 12:20|          2|
|      1|2020-08-19 14:20|          2|
|      1|2020-08-23 09:20|          1|
|      2|2020-08-24 08:00|          1|
+-------+----------------+-----------+

要获得每位客户最多5天的访问次数，您可以执行以下操作：

df.withColumn('5_day_visit', F.count("*").over(w)).drop('date_long')\
    .groupBy('cust_id').agg(F.max('5_day_visit').alias('max_5_day_visits')).show()
+-------+----------------+                                                      
|cust_id|max_5_day_visits|
+-------+----------------+
|      1|               4|
|      2|               1|
+-------+----------------+