Help Please - Modification of SUM formula - same cell across multiple tabs

[diecast61]

Hi All --

I've run across something I can use your help with.

I know the formula to add the same cell across multiple contiguous sheets is:
=SUM('Sheet1:Sheet5'!B5)

which addes the value in B5 across all sheets between 1 and 5

I'd like to be able to have the user select the 1st sheet in the range and last sheet in the range - using 2 dropdowns for the tab names. Let's say Tab 1 ..... Tab 15 are the tab names.

Now in cell A1 I have a dropdown and the user selects the 1st Tab in the range: Lets Say Tab 3
In cell A2 is the second dropdown and they select Tab 7

OK - what is the proper format to reference A1 and A2 in the =SUM('Sheet1:Sheet5'!B5)
so that I don't get a #REF, #NAME, #VALUE?

I know I'm missing something -- but can't figure it out.

The dropdowns are on teh summary sheet - along with A1, A2.

Thanks in advance for any help you can lend. This one has me stumpted.

If this isn't clear - let me know and I will try to clarify.