Welcome! I'd recommend that you post your specific questions in the K-5 forum so that you can get a more through reply.
If you'd like to stay within that budget, then the Tamron 70-200mm F2.8 lens would be an excellent choice for sports:
Tamron 70-200mm f/2.8 Di LD (IF) Macro AF Lens AF001P-700 B&H
You could also get the Pentax 55-300mm, but it is a bit slower, after all.
Adam
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