Getting a the max value of an array of the sums of multiple columns? Is it possible?

Having a hard time thinking of a method of doing this within a single cell. Hopefully you guys/gals can help. Basically what I am looking to do is find a way to create a dynamic array of the sums of individual columns and return the maximum value in that array. Below is the best I could come up with but it is only dynamic in height. I would like the quantity of columns to also be dynamic. The example code below is using a range of A1:E5. An example would be if each column is a Day and each row is a quantity I want to know what the maximum total quantity for a single day is.

=MAX(
SUM(OFFSET(A1,0,0,Num_Of_Rows)),
SUM(OFFSET(A1,0,1,Num_Of_Rows)),
SUM(OFFSET(A1,0,2,Num_Of_Rows)),
SUM(OFFSET(A1,0,3,Num_Of_Rows)),
SUM(OFFSET(A1,0,4,Num_Of_Rows)))

The easy way would be to have an additional row of totals and which have a dynamic height [i.e. =sum(offset(A1,0,0,Num_Of_Rows))] and then use a separate cell to set a dynamic width across the total row for the maximum [i.e. =max(offset(A6,0,0,0,Num_Of_Columns))] but I don't have the ability to have a totals row here.

Hopefully there is another solution you can help me find. Thanks.

FYI this has been crossposted here:
Getting a the max value of an array of the sums of multiple columns? Is it possible?