Best solution: use a global hash.

Otherwise, just declare them at the top of your program, and make call_variables update them. Don't put my $one = ... inside the function because that would create lexicals in the scope of the function body (not what you want).

With hash:

# [at the top, before subroutine definitions and code]
my %my_vars;
# [...]

sub call_variables {
  #pick up a string I've passed from previous program via 'spec_vars'
  my $spec_vars = param('spec_vars');
  @my_vars{qw/one two three four five/} = split /~/, $spec_vars;
}
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With globals (file-scoped lexicals, not dynamic variables):

# [at the top, before subroutine definitions and code]
my ($one, $two, $three, $four, $five);
# [...]

sub call_variables {
  #pick up a string I've passed from previous program via 'spec_vars'
  my $spec_vars = param('spec_vars');
  ($one, $two, $three, $four, $five) = split /~/, $spec_vars;
}
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If you don't want to declare them, you have to use fully scoped package variable names such as $::one under use strict. The variables will be dynamic, of course.

Update: replaced @my_vars{one, two, three, four, five} with @my_vars{qw/one two three four five/}