Something like this? I made a list to hold the players hands, you can use their names for indexing.
Every time you deal you have to remove the cards from the deck, as well as add them to the players hands.
set.seed(1)
cards <- 1:52
players <- letters[1:5]
hands <- vector("list", length(players))
names(hands) <- players
for (i in players){
deal <- sample(cards, 5)
cards <- setdiff(cards, deal)
hands[[i]] <- deal
}
hands
#> $a
#> [1] 4 39 1 34 23
#>
#> $b
#> [1] 48 16 20 37 24
#>
#> $c
#> [1] 27 12 9 11 18
#>
#> $d
#> [1] 32 38 49 51 25
#>
#> $e
#> [1] 2 33 5 8 15
Created on 2021-03-08 by the reprex package (v1.0.0)