I have a mysql table with the following data in it:

user_id score
1234 28
4654 -15
5986 15
3657 10

If i have PHP select the score column for user 5986 how could i then have PHP calculate the next highest score in the MySQL table ?

Why not just have SQL server to do that? That's exactly the kind of thing it excels at! AND it's much quicker than switching to PHP for sorting.

get the "top" scorer

SELECT userid FROM table MAX(score);

second highest

SELECT userid FROM table ORDER BY score ASC LIMIT 1,1;