If you want to retrieve both the number of results found as well as limiting the number to 5, you will probably have to do two queries. The first would be like:
$sql="SELECT Name FROM sexoffenders";
// this query gets the number of rows in the result
$sql . = "WHERE COUNT(*) LIKE '%".$_GET['search_text']."%'
OR AKA LIKE '%".$_GET['search_text']."%'
OR Address LIKE '%".$_GET['search_text']."%'
OR Conviction LIKE '%".$_GET['search_text']."%'
OR Description LIKE '%".$_GET['search_text']."%'
OR Victim LIKE '%".$_GET['search_text']."%'
OR Comments LIKE '%".$_GET['search_text']."%'
";
$results=mysql_query($sql);
$numRows=$results[0];
$numPages = ceil($numRows / 5);
The second query would be used to retrieve the next five rows, starting at $offset. It is probably easiest to pass $offset in the URL (using the $_GET parameter), so that your links can be like http://www.mydomain.com/page.php?offest=0,
http://www.mydomain.com/page.php?offset=5,
etc.
$sql="SELECT Name, AKA, DOB, Address, Conviction, Description, Victim, Comments, Pic FROM sexoffenders";
// this query gets the next five rows in the result
$sql1 . = "WHERE COUNT(*) LIKE '%".$_GET['search_text']."%'
OR AKA LIKE '%".$_GET['search_text']."%'
OR Address LIKE '%".$_GET['search_text']."%'
OR Conviction LIKE '%".$_GET['search_text']."%'
OR Description LIKE '%".$_GET['search_text']."%'
OR Victim LIKE '%".$_GET['search_text']."%'
OR Comments LIKE '%".$_GET['search_text']."%'
" ORDER BY Name LIMIT $offset, 5";
$results=mysql_query($sql2);
EDIT: I didn't check all the single and double quote marks to make sure they are correct, so be careful before you paste.