Splitting a string in an SQL query

Hmm... Not sure how much faster this will be, but it may be easier to wrap your head around.
You can use a recursive CTE:

WITH Splitter (id, start, e, section, original, num) as (
               SELECT id, 1, CHARINDEX('-', budgetCode), CAST('' AS VARCHAR(20)), budgetCode, 0
               FROM PC
               UNION ALL
               SELECT id, e + 1, 
                      CASE WHEN CHARINDEX('-', original, e + 1) > 0
                           THEN CHARINDEX('-', original, e + 1)
                           ELSE LEN(original) + 1 END,
                      SUBSTRING(original, start, e - start), 
                      original, num + 1
               FROM Splitter
               WHERE e > start) 

Results:

SELECT * 
FROM splitter

Makes a table that looks like this:

Id  BudgetCode
=====================
1   xxxx-yyyyy-zzzzz

Into this:

Id  Start  End   Section   Original           Num
1   1      5               xxxx-yyyyy-zzzzz   0
1   6      11     xxxx      xxxx-yyyyy-zzzzz   1
1   12     17    yyyyy     xxxx-yyyyy-zzzzz   2
1   18     17    zzzzz     xxxx-yyyyy-zzzzz   3

SQL Fiddle Example

You can then join to the result set multiple times based on Num or something to get the particular index you need. It'll automatically handle any additional 'subfields' (to the limit of the recursion, of course).

First, if you have any influence at all in the database design, you may do better by storing the strings separately. It is a lot easier to glue strings together when needed than to split them apart when needed.

Second, if you are guaranteed to always have the same number of digits in each budget code, you could just use the absolute character positions, such as substring(pc.BudgetCode,6,5)

See this similar SO question and this more general SO question, which links to this authoritative page of many ways to split strings, many of which seem unnecessarily complex for your purpose.

You might also try writing really simple functions. One advantage is that MSSQL seems to cache the results of functions, so a query with functions can run a lot faster the second time:

create function getslidcode (@budgetcode nvarchar(100))
  returns @slidcode nvarchar(100) as
begin
  declare @pos int
  select @pos = charindex('-', @budgetcode)
  select @pos = charindex('-', @budgetcode, @pos + 1)
  select @slidcode = substring(@budgetcode, @pos + 1, 100)
end

select budgetcode, getslidcode(budgetcode) as slidcode from pc