The resources are 1, 2, 3, 4, 5 where 5 represents Ore.

The idea is to first count the resources by type, then reduce all counts of B, L, W, and S by one - if we counted none for any of these four then they will now have entries of -1 - we need to acquire them from our remaining resources (This is actually achieved by adding an extra O and reducing all counts by 1). Next we integer-divide all these values by four to see how many units we may trade for with each of our resource types while not affecting the -1 and 0 counts (note that -1 integer-divided by four is -1, not 0). Add up the values and check if it is greater than or equal to zero (here greater than -1 can be used since we always have integers):

The resources are 1, 2, 3, 4, 5 where 5 represents Ore.

The idea is to first count the resources by type, then reduce all counts of B, L, W, and S by one - if we counted none for any of these four then they will now have entries of -1 - we need to acquire them from our remaining resources (This is actually achieved by adding an extra O (5) and reducing all five counts by 1). Next we integer-divide all these values by four to see how many units we may trade for with each of our remaining counts by resource type while not affecting the -1 and 0 counts (note that -1 integer-divided by four is -1, not 0). Lastly we add up the values and check if the result is greater than or equal to zero (here greater than -1 can be used since we always have integers).

Jelly, 13 bytes

ċЀ5’‘5¦:4S>-

Try it online! or see the test-suite (using the OP IO).

First count the resources by type. Then reduce all of B, L, W, and S by one - if we counted none for any of these four then they will now have entries of -1 - we need to acquire them from our remaining resources. Integer-divide all these values by four to see how many units we may trade for with each of our resource types while not affecting the -1 and 0 counts (note that -1 integer-divided by four is -1, not 0). Add up the values and check if it is greater than or equal to zero (here greater than -1 can be used since we always have integers):

ċЀ5’‘5¦:4S>- - Link: list of numbers (BLWSO:12345) e.g. [3,2,2,2,2,2,5,5,5,5] (WLLLLLOOOO)
   5          - literal 5
 Ѐ           - map across implicit range(5) = [1,2,3,4,5]:
ċ             -   count                                  [ 0, 5, 1, 0, 4]
    ’         - decrement (vectorises)                   [-1, 4, 0,-1, 3]
       ¦      - sparse application:
      5       - ...to indices: 5
     ‘        - ...action: increment                     [-1, 4, 0,-1, 4]
        :4    - integer divide by four                   [-1, 1, 0,-1, 1]
          S   - sum                                      0
            - - literal -1                              -1
           >  - greater than?                            1

Jelly,  13  12 bytes

;5ċЀ5’:4S>-

Try it online! or see the test-suite (using the OP IO).

The idea is to first count the resources by type, then reduce all counts of B, L, W, and S by one - if we counted none for any of these four then they will now have entries of -1 - we need to acquire them from our remaining resources (This is actually achieved by adding an extra O and reducing all counts by 1). Next we integer-divide all these values by four to see how many units we may trade for with each of our resource types while not affecting the -1 and 0 counts (note that -1 integer-divided by four is -1, not 0). Add up the values and check if it is greater than or equal to zero (here greater than -1 can be used since we always have integers):

;5ċЀ5’:4S>- - Link: list of numbers (BLWSO:12345) e.g. [3,2,2,2,2,2,5,5,5,5] (WLLLLLOOOO)
;5           - concatenate a five                       [3,2,2,2,2,2,5,5,5,5,5]
     5       - literal 5
   Ѐ        - map across implicit range(5) = [1,2,3,4,5]:
  ċ          -   count                                  [ 0, 5, 1, 0, 5]
      ’      - decrement (vectorises)                   [-1, 4, 0,-1, 4]
       :4    - integer divide by four                   [-1, 1, 0,-1, 1]
         S   - sum                                      0
           - - literal -1                              -1
          >  - greater than?                            1

How?

First count the resources by type. Then reduce all of B, L, W, and S by one - if we counted none for any of these four then they will now have entries of -1 - we need to acquire them from our remaining resources. Integer-divide all these values by four to see how many units we may trade for with each of our resource types while not affecting the -1 and 0 counts (note that -1 integer-divided by four is -1, not 0). Add up the values and check if it is greater than or equal to zero (here greater than -1 can be used since we always have integers):

ċЀ5’‘5¦:4S>- - Link: list of numbers (BLWSO:12345) e.g. [3,2,2,2,2,2,5,5,5,5] (WLLLLLOOOO)
   5          - literal 5
 Ѐ           - map across implicit range(5) = [1,2,3,4,5]:
ċ             -   count                                  [ 0, 5, 1, 0, 4]
    ’         - decrement (vectorises)                   [-1, 4, 0,-1, 3]
       ¦      - sparse application:
      5       - ...to indices: 5
     ‘        - ...action: increment                     [-1, 4, 0,-1, 4]
        :4    - integer divide by four                   [-1, 1, 0,-1, 1]
          S   - sum                                      0
            - - literal -1                              -1
           >  - greater than?                            1