tidyeval was introduced in dplyr 0.7.0, if you want to program with dplyr 0.5.0 you will probably need to use the functions with underscores after them (i.e. mutate_() - I am not sure the naming convention for these functions.) These will let you pass character strings to the functions so you can create generic functions with them. However, you won't be able to use quosures with these functions (at least not to my knowledge)
Also, does the code have to run under a different account than your own on the server? Or do you have policies in place that prevent non-approved packages? Otherwise, I think you should be able to install an updated version of the package in your local package directory, just like you would for a package that you are missing.
Which package requires a newer version? dplyr only requires 3.1.2 or newer, though I suspect one or two dependencies may require a newer version. You may still be able to work around that by carefully installing appropriate older versions, though.
In the help for the rlang functions, they mention which base R function the new functions are based on. Using that I tried my best at getting you some working code, hopefully this gets you going: