in R group service to order numbers within a range in a dataframe

I have a dataframe of a service. Now I need to add a column "order" and group them with the following rule:

Group the service to orders: If within the next 5 values after one service Value "A" is another service "A" present, fill all values to an order ID - also the ones that don't have a service value. If there is no service value within the next 5 values the next order group is defined.

id   time       apples   service
1    13:20:01   2        
2    13:20:02   2        A         
3    13:20:03   2        A         
4    13:20:04   3                  
5    13:20:05   3        A         
6    13:20:06   2                  
7    13:20:07   2        A         
8    13:20:08   2        A         
9    13:20:09   2                  
10   13:20:10   2                 
11   13:20:11   2                 
12   13:20:12   2
14   13:20:13   2        A         
15   13:20:14   2                  
16   13:20:15   2        A         

This is the format I'm looking for. ID 2 to ID 8 is an order and ID 14 to ID 16.

id   time       apples   service  Order
1    13:20:01   2        
2    13:20:02   2        A         1
3    13:20:03   2        A         1
4    13:20:04   3                  1
5    13:20:05   3        A         1
6    13:20:06   2                  1
7    13:20:07   2        A         1
8    13:20:08   2        A         1
9    13:20:09   2                  
10   13:20:10   2                 
11   13:20:11   2                 
12   13:20:12   2
14   13:20:13   2        A         2
15   13:20:14   2                  2
16   13:20:15   2        A         2

I tried it with a for loop. I suggests there is a way to use the mutate method and add the "range" conditon.

Thx for your help!