Need an algorithm to take data from 5 columns in a specific order to create a new variable

When in doubt, it always helps to start with some data and torture it into a usable form to be able to create a reproducible example, called a reprex to illuminate the problem.

There's no better place to start than mtcars. Granted it deals with automobiles, but you can use it to create a dummy data set for your problem:

suppressPackageStartupMessages(library(dplyr))
exemplar <- mtcars %>% select(1:5)
rownames(exemplar) <- seq(1:nrow(exemplar))
exemplar <- exemplar %>% 
  mutate(mpg = ifelse(mpg < 20, 1, 0)) %>% 
  mutate(cyl = ifelse(cyl < 6, 1, 0)) %>% 
  mutate(disp = ifelse(disp < 200, 1, 0)) %>% 
  mutate(hp = ifelse(hp < 150, 1, 0)) %>% 
  mutate(drat = ifelse(drat < 3, 1, 0))
colnames(exemplar) <- c("Drug1","Drug2","Drug3","Drug4","Drug5")
exemplar
#>    Drug1 Drug2 Drug3 Drug4 Drug5
#> 1      0     0     1     1     0
#> 2      0     0     1     1     0
#> 3      0     1     1     1     0
#> 4      0     0     0     1     0
#> 5      1     0     0     0     0
#> 6      1     0     0     1     1
#> 7      1     0     0     0     0
#> 8      0     1     1     1     0
#> 9      0     1     1     1     0
#> 10     1     0     1     1     0
#> 11     1     0     1     1     0
#> 12     1     0     0     0     0
#> 13     1     0     0     0     0
#> 14     1     0     0     0     0
#> 15     1     0     0     0     1
#> 16     1     0     0     0     0
#> 17     1     0     0     0     0
#> 18     0     1     1     1     0
#> 19     0     1     1     1     0
#> 20     0     1     1     1     0
#> 21     0     1     1     1     0
#> 22     1     0     0     0     1
#> 23     1     0     0     0     0
#> 24     1     0     0     0     0
#> 25     1     0     0     0     0
#> 26     0     1     1     1     0
#> 27     0     1     1     1     0
#> 28     0     1     1     1     0
#> 29     1     0     0     0     0
#> 30     1     0     1     0     0
#> 31     1     0     0     0     0
#> 32     0     1     1     1     0

Created on 2019-12-25 by the reprex package (v0.3.0)

I've chosen 1/0 in place of yes/no in @FJCC's example, because there are advantages for when you need to use linear algebra, which isn't as scary as it might sound.

Given the faked exemplar data set ,

rescue <- exemplar %>% mutate(rescue = ifelse(
                        Drug1 == 1 & Drug2 == 1 |
                        Drug2 == 1 & Drug3 == 1 |
                        Drug3 == 1 & Drug4 == 1 |
                        Drug4 == 1 & Drug5 == 1,
                        1,0))
rescue
#>    Drug1 Drug2 Drug3 Drug4 Drug5 rescue
#> 1      0     0     1     1     0      1
#> 2      0     0     1     1     0      1
#> 3      0     1     1     1     0      1
#> 4      0     0     0     1     0      0
#> 5      1     0     0     0     0      0
#> 6      1     0     0     1     1      1
#> 7      1     0     0     0     0      0
#> 8      0     1     1     1     0      1
#> 9      0     1     1     1     0      1
#> 10     1     0     1     1     0      1
#> 11     1     0     1     1     0      1
#> 12     1     0     0     0     0      0
#> 13     1     0     0     0     0      0
#> 14     1     0     0     0     0      0
#> 15     1     0     0     0     1      0
#> 16     1     0     0     0     0      0
#> 17     1     0     0     0     0      0
#> 18     0     1     1     1     0      1
#> 19     0     1     1     1     0      1
#> 20     0     1     1     1     0      1
#> 21     0     1     1     1     0      1
#> 22     1     0     0     0     1      0
#> 23     1     0     0     0     0      0
#> 24     1     0     0     0     0      0
#> 25     1     0     0     0     0      0
#> 26     0     1     1     1     0      1
#> 27     0     1     1     1     0      1
#> 28     0     1     1     1     0      1
#> 29     1     0     0     0     0      0
#> 30     1     0     1     0     0      0
#> 31     1     0     0     0     0      0
#> 32     0     1     1     1     0      1

Created on 2019-12-25 by the reprex package (v0.3.0)

ifelse is a logical test in a series of | OR operators that looks at successive pairs of the Drug_i columns to see if there is a 1 followed by a 1 in any of the pairs: 1:2, 2:3, 3:4, or 4:5.