Some example data. Note that I turned the rownames from your example into a column called 'rowid'.

before <- structure(list(rowid = c("r1", "r1", "r1", "r1", "r1", "r2",
"r2", "r2", "r2", "r2"), s1 = c(0L, 3L, 5L, 20L, 15L, 12L, 18L,
15L, 20L, 17L), s2 = c(16L, 13L, 11L, 1L, 18L, 20L, 0L, 3L, 7L,
4L), s3 = c(15L, 7L, 16L, 20L, 1L, 7L, 14L, 6L, 5L, 10L), s4 = c(14L,
10L, 5L, 7L, 18L, 14L, 20L, 1L, 10L, 12L), s5 = c(4L, 9L, 5L,
9L, 7L, 9L, 2L, 5L, 0L, 19L)), row.names = c(NA, -10L), class = c("tbl_df",
"tbl", "data.frame"))

> before
   rowid s1 s2 s3 s4 s5
1     r1  0 16 15 14  4
2     r1  3 13  7 10  9
3     r1  5 11 16  5  5
4     r1 20  1 20  7  9
5     r1 15 18  1 18  7
6     r2 12 20  7 14  9
7     r2 18  0 14 20  2
8     r2 15  3  6  1  5
9     r2 20  7  5 10  0
10    r2 17  4 10 12 19

tidyverse solution

library("dplyr")

after <- before %>%
  group_by(rowid) %>%
  summarize(across(everything(), max))

> after
# A tibble: 2 x 6
  rowid    s1    s2    s3    s4    s5
  <chr> <int> <int> <int> <int> <int>
1 r1       20    18    20    18     9
2 r2       20    20    14    20    19

data.table solution. This will be quicker and more memory efficient if you have a lot of data and/or limited resources.

library("data.table")

setDT(before)
after <- before[, lapply(.SD, max), by=rowid]

> after
   rowid s1 s2 s3 s4 s5
1:    r1 20 18 20 18  9
2:    r2 20 20 14 20 19

with datamash:

input:

$ cat file.txt 

rowid   s1  s2  s3  s4  s5
r1  0   16  15  14  4
r1  3   13  7   10  9
r1  5   11  16  5   5
r1  20  1   20  7   9
r1  15  18  1   18  7
r2  12  20  7   14  9
r2  18  0   14  20  2
r2  15  3   6   1   5
r2  20  7   5   10  0
r2  17  4   10  12  19

output:

$ datamash -sH -g1 max 2-6 < file.txt 

GroupBy(rowid)  max(s1) max(s2) max(s3) max(s4) max(s5)
r1  20  18  20  18  9
r2  20  20  14  20  19