Let's solve it with a simple? regex :)

#!/usr/bin/perl -l

# http://perlmonks.org/?node_id=1207373

use strict; # regex Parks Puzzle
use warnings;
use re 'eval';

print "Initial grid:\n\n", my $board = <<END;
GRBBB
GRBBW
ORBBW
OOOWW
OOOOW
END

my $N = $board =~ /\n/ && $-[0];
my @letters = sort keys %{{ map {;$_, $_} $board =~ /\w/g }};
my @squares;
push @squares, "$&" . $` =~ tr/\n// . ',' . length($`) % ($N + 1)
  while $board =~ /\w/g;
$_ = join ' ', sort @squares;        # string to be matched
print "String to be matched (color,row,col):\n\n$_";

my $count = 0;
my $regex = '';
for my $color ( @letters )
  {
  my $y = 2 * $count + 1;
  my $x = $y + 1;
  $count and $regex .= ".*\n";
  $regex .= "$color(\\d+),(\\d+)\\b\n";
  my @tests;
  for my $prev ( 0 .. $count - 1 )
    {
    my $yy = 2 * $prev + 1;
    my $xx = $yy + 1;
    push @tests, "\$$yy == \$$y", "\$$xx == \$$x",    # same row & sam
+e col
      "abs \$$yy - \$$y < 2 && abs \$$xx - \$$x < 2"  # diagonal neigh
+bor
      ;
    }
  @tests and $regex .= "(??{" . join(' || ', @tests) . " ? 'fail' : ''
+})\n";
  $count++;
  }
print "\nRegex (match one of each color with conditions):\n\n$regex";

my $matches = join ' ', /$regex/x;             # let regex do the hard
+ work
print "Captures from regex (row,col pairs of solution):\n\n$matches\n"
+;

my $grid = $board =~ s/\w/-/gr;                  # build grid & insert
+ answer
substr $grid, $1 * ($N + 1) + $2, 1, shift @letters
  while $matches =~ /(\d+) (\d+)/g;
print "Formatted solution:\n\n$grid";
[download]

Outputs:

Initial grid:

GRBBB
GRBBW
ORBBW
OOOWW
OOOOW

String to be matched (color,row,col):

B0,2 B0,3 B0,4 B1,2 B1,3 B2,2 B2,3 G0,0 G1,0 O2,0 O3,0 O3,1 O3,2 O4,0 
+O4,1 O4,2 O4,3 R0,1 R1,1 R2,1 W1,4 W2,4 W3,3 W3,4 W4,4

Regex (match one of each color with conditions):

B(\d+),(\d+)\b
.*
G(\d+),(\d+)\b
(??{$1 == $3 || $2 == $4 || abs $1 - $3 < 2 && abs $2 - $4 < 2 ? 'fail
+' : ''})
.*
O(\d+),(\d+)\b
(??{$1 == $5 || $2 == $6 || abs $1 - $5 < 2 && abs $2 - $6 < 2 || $3 =
+= $5 || $4 == $6 || abs $3 - $5 < 2 && abs $4 - $6 < 2 ? 'fail' : ''}
+)
.*
R(\d+),(\d+)\b
(??{$1 == $7 || $2 == $8 || abs $1 - $7 < 2 && abs $2 - $8 < 2 || $3 =
+= $7 || $4 == $8 || abs $3 - $7 < 2 && abs $4 - $8 < 2 || $5 == $7 ||
+ $6 == $8 || abs $5 - $7 < 2 && abs $6 - $8 < 2 ? 'fail' : ''})
.*
W(\d+),(\d+)\b
(??{$1 == $9 || $2 == $10 || abs $1 - $9 < 2 && abs $2 - $10 < 2 || $3
+ == $9 || $4 == $10 || abs $3 - $9 < 2 && abs $4 - $10 < 2 || $5 == $
+9 || $6 == $10 || abs $5 - $9 < 2 && abs $6 - $10 < 2 || $7 == $9 || 
+$8 == $10 || abs $7 - $9 < 2 && abs $8 - $10 < 2 ? 'fail' : ''})

Captures from regex (row,col pairs of solution):

1 3 0 0 4 2 2 1 3 4

Formatted solution:

G----
---B-
-R---
----W
--O--
[download]

---

---

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