How do I include a 'between two dates' IF AND formula inside of a SUMIFS formula?

I am doing a personal budgeting project. I have 2 excel files - 1 is detail of my last 5 years banking activity, the other is an annual monthly summary and analysis (S/A) file - so 12 worksheets inside the one workbook.

I am trying to find a way to make the S/A file more dynamic so I can copy 1 formula to the various fields that look up and sum detail activity equal to or after the first date but before the 2nd date BUT ONLY for lines that match the category found in Column B of the S/A file worksheet. This gives me the activity in my budget categories between 1 paydate and the day before the next paydate.

Example: I want to find and sum all the amounts (Detail file $F:$F) in my detail file that are for Cell Phone payments (Detail File $E:$E, matching S/A field B6) where the transaction date (Detail file $A:$A) is on or after 7/14/2017 (start Date, S/A field E5) but before 7/28/2017 (end date, S/A field E33).

This is what I have tried:

=IF(AND('[2016-Present Bank Statements.xlsx]Checking TRX'!$A$2:$A$2959>(E5-1),'[2016-Present Bank Statements.xlsx]Checking TRX'!$A$2:$A$2959<E33),SUMIF('[2016-Present Bank Statements.xlsx]Checking TRX'!$E$2:$E$2959,B6,'[2016-Present Bank Statements.xlsx]Checking TRX'!$F$1:$F$2959),0)

I was getting an error trying to put ">=" into the first component so I put the cell reference -1 to get the previous date from my starting date. So anything greater than E5-1 should include the date in E5 (because let's face it, we all go mad spending on payday).

=SUMIFS('[2016-Present Bank Statements.xlsx]Checking TRX'!$F:$F,'[2016-Present Bank Statements.xlsx]Checking TRX'!$E:$E,B6,'[2016-Present Bank Statements.xlsx]Checking TRX'!$A:$A,"E5≤x<E33")

The last part "E5≤x<E33" I found on the interwebs for comparing dates.

I have tried breaking out the greater than/equal to and less than statements into 2 criteria in a SUMIFS, but no luck.

I either get back 0.00 or #SPILL

These are the headers in my details file. Do I need to rearrange them to get either of these formulas to pick up the right amount?

Date|Account|Merchant|Description|Category|Amount

My current process is to do a SUMIF but have it reference the specific lines that related to the start and end dates. I've gotten off somehow between yesterday and today and don't want to redo all my tabs so far.

=-SUMIF('[2016-Present Bank Statements.xlsx]Checking TRX'!$E$2076:$E$2168,B6,'[2016-Present Bank Statements.xlsx]Checking TRX'!$F$2076:$F$2168)

Please help!!!