Here are a few general guidelines which you may find useful (followed by code which incorporates them):

• KISS! Be specific when you can, to avoid false positives. In this case, using a character class to find "Wilma" | "wilma" lends itself to all manner of false positives... for example "Selma."
• Be wary of \b and friends: they won't do what you expect unless you are very clear about the meanings of \w and \W. ikegami explains your specific problem, above.
• Do learn to use regex modifiers such as /.../i to help you simplify your regexen.

So, using your data (and adding the "... saw Wilma yesterday" part of the exercise statement):

while(<DATA>) {

  chomp;
  if ( /(Wilma)([\w\W]{5})/i ) {
    print "Matched: |<$1> <$2>\n";
  } else { 
    print "No match: |$_|\n";
  }
}

__DATA__
This is a line that has the name fred in it.
This is a line that does not.
This is a line that has the name barney in it.
This is fred.
This is notfred.
Hello Fred Flintstone!
Hello Fred!
Allo allo, Alfred!
Cheerio Mr. frederick!
Hello Mr. Slate!
Hello FRED!
Hello Fred!
Hello fred!
This is some wilma text with some words in it this is fred.
This is wilmafred.
This is some more wilma text fred.
Mrs. Wilma Flintstone
wilma&fred
wilma but not barney
I saw Wilma yesterday.
[download]

Output:

perl 732070.pl
No match: |This is a line that has the name fred in it.|
No match: |This is a line that does not.|
No match: |This is a line that has the name barney in it.|
No match: |This is fred.|
No match: |This is notfred.|
No match: |Hello Fred Flintstone!|
No match: |Hello Fred!|
No match: |Allo allo, Alfred!|
No match: |Cheerio Mr. frederick!|
No match: |Hello Mr. Slate!|
No match: |Hello FRED!|
No match: |Hello Fred!|
No match: |Hello fred!|
Matched: |<wilma> < text>
Matched: |<wilma> <fred.>
Matched: |<wilma> < text>
Matched: |<Wilma> < Flin>
Matched: |<wilma> <&fred>
Matched: |<wilma> < but >
Matched: |<Wilma> < yest>
[download]

Caveat: Neither my Llama nor my Camel edition has the exercise you describe, so this may miss a requirement that [Ww]ilma be followed by a space or by a punctuation mark or symbol, which would substantially change the regex required.

Update: ...and, oh yes, I've simplified your print "Matched.... as well, again in the pursuit of KISS.