Appending/subsearches can be pretty expensive in terms of performance and sometimes pretty hard to keep track of. What you probably need here is to run a single search over the last 5 weeks (or days, or whatever your window is) BUT scope it to the right hour interval. For example, this search will go back 5 days, search only between 9pm and 10pm and chart the count of events per method (GET or POST) for said slot of each day:
index=_internal source=*access* date_hour=21 earliest=-5d | chart count over method by date_mday
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