Some pseudo code for you:
1. Get Rank of Person
SELECT rank, name FROM users WHERE name='$search' LIMIT 1
2. Calculate Min and Max rank
$rank_max = $rank + 3;
$rank_min = $rank - 2;
3. Get Range of People
SELECT rank, name FROM users WHERE rank < $rank_max AND rank > $rank_min LIMIT 5
Get what I mean?