That's surprising. It works for me, as illustrated below:
# what you did
as.POSIXct(x = "02:27:16 05-Mar-2019",
tz = "",
format = "%H:%M:%S %m/%d/%Y")
#> [1] NA
# the above expects date in this form: "02:27:16 03/05/2019"
# what I did
as.POSIXct(x = "02:27:16 05-Mar-2019",
format = "%H:%M:%S %d-%b-%Y")
#> [1] "2019-03-05 02:27:16 UTC"
# this one expects date in this form: "02:27:16 05-Mar-2019"
Can you please provide a REPRoducible EXample of your problem of getting NA using my code?
In case you don't know how to make a reprex, here's a great link: