In dplyr, how can I sample rows in a dataframe with conditions (sum and min) applied to one or more columns?

I have data that looks like this:

Object  Rank    Cost
OBJ1    1       3
OBJ2    2       3
OBJ3    3       2.5
OBJ4    4       1.5
OBJ5    5       0
OBJ6    6       1
OBJ7    7       0
OBJ8    8       0
OBJ9    9       1
OBJ10   10      0
OBJ11   11      2
OBJ12   12      1
OBJ13   13      2.5
OBJ14   14      1
OBJ15   15      1
OBJ16   16      3
OBJ17   17      0
OBJ18   18      0
OBJ19   19      0

      

        
        
        
      

    

I want to use dplyr to randomly select 5 rows so that the sum of the cost column for those 5 rows is exactly 5 and the sum of the rank for the 5 samples taken is the smallest possible. This is a simplified example, but my actual data has a lot more rows. Any ideas how to do this without writing a loop?

Here's the data:

x <- structure(list(Object = structure(c(1L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L), 
    .Label = c("OBJ1", "OBJ10", "OBJ11", "OBJ12", "OBJ13", "OBJ14", "OBJ15", "OBJ16", "OBJ17", "OBJ18", "OBJ19", "OBJ2", "OBJ3", "OBJ4", "OBJ5", "OBJ6", "OBJ7", "OBJ8", "OBJ9"), class = "factor"), 
    Rank1 = 1:19, Cost = c(3, 3, 2.5, 1.5, 0, 1, 0, 0, 1, 0, 2, 1, 2.5, 1, 1, 3, 0, 0, 0)), 
    .Names = c("Object", "Rank1", "Cost"), class = "data.frame", row.names = c(NA, -19L))