Please please help with this simple but long request!!

I have a workbook with multiple named worksheets. In the "summary" worksheet
I have a list of the names of each worksheet. I am trying to use this list to
construct multiple =sum functions each of which refers to a particular named
worksheet, but don't want to type in the name of each worksheet manually.

As an example imagine that there is a worksheet named Leicester and this
name is sitting in cell A1 of the "summary" worksheet. I want to sum the
cells B1 to B5 in the leicester worksheet. I tried to write the following
=SUM(cell("contents",A1)!B1:B5) which does not work.

The problem seems to be how to use the text returned from the cell function
(or t function) as actual text so that it attaches to ! to reference the
appropriate cell.