Pyth, 9 bytes

ehc2osNyQ

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[1, 2, 4]

Demonstration.

ehc2osNyQ
             Q = eval(input())
       yQ    Take all subsets of Q.
    osN      Order those element lists by their sums.
  c2         Cut the list in half.
eh           Take the last element of the first half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split. We extract the first of those two elements and print it.

Pyth, 9 bytes

ehc2osNyQ

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[1, 2, 4]

Demonstration.

ehc2osNyQ
             Q = eval(input())
       yQ    Take all subsets of Q.
    osN      Order those element lists by their sums.
  c2         Cut the list in half.
eh           Take the last element of the first half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split. We extract the first of those two elements and print it.

Pyth, 15 13 12

@Vc2osNyQtM2

1 byte thanks to Jakube

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[[1, 2, 4], [3, 5]]

Demonstration.

@Vc2osNyQtM2
                Q = eval(input())
       yQ       Take all subsets of Q.
    osN         Order those element lists by their sums.
  c2            Cut the list in half.
         tM2    The list [-1, 0]
@V              Vectorize "@", the lookup function, over these two lists.
                This returns the last element of the first half and
                the first element of the second half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split.

If it's only necessary to output the bags carried in one of the two hands, the following code is sufficient:

Pyth, 9 bytes

hec2osNyQ

Pyth, 9 bytes

ehc2osNyQ

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[1, 2, 4]

Demonstration.

ehc2osNyQ
             Q = eval(input())
       yQ    Take all subsets of Q.
    osN      Order those element lists by their sums.
  c2         Cut the list in half.
eh           Take the last element of the first half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split. We extract the first of those two elements and print it.

Pyth, 15 13

heJc2osNyQehJ

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[3, 5]
[1, 2, 4]

Demonstration.

heJc2osNyQehJ
                 Q = eval(input())
        yQ       Take all subsets of Q.
     osN         Order those element lists by their sums.
   c2            Cut the list in half.
  J              Save it to J.
he               Print the first element of the second half.
          ehJ    Print the last element of the first half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split.

If it's only necessary to output the bags carried in one of the two hands, the following code is sufficient:

Pyth, 9 bytes

hec2osNyQ

Pyth, 15 13 12

@Vc2osNyQtM2

1 byte thanks to Jakube

Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[[1, 2, 4], [3, 5]]

Demonstration.

@Vc2osNyQtM2
                Q = eval(input())
       yQ       Take all subsets of Q.
    osN         Order those element lists by their sums.
  c2            Cut the list in half.
         tM2    The list [-1, 0]
@V              Vectorize "@", the lookup function, over these two lists.
                This returns the last element of the first half and
                the first element of the second half.

This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split.

If it's only necessary to output the bags carried in one of the two hands, the following code is sufficient:

Pyth, 9 bytes

hec2osNyQ