i need to apply for an HK visa from Singapore for 5 days

It may take one to two weeks if you apply for the Hk visa through the China Embassy in Singapore. Ot you may also post your application to your local sponsor in the HKSAR and entrust him/her to apply for the visa for you, which may take less time.

Based on your travel purpose, I think you may just apply for a Hk transit visa with the documents below:
1. fulfilled Hk visa application form ID 1003A
2. your valid passport
3. your singaporean student permit
4. your financial standing, e.g. bank statements, savings accounts passbooks, tax receipts
5. transportation arrangement, e.g. flight itinerary
6. proof of the proposed leisure visit to Hong Kong
7. confirmed seats to the next destination after visiting Hong Kong
8. Hk visa application form ID 1003B from your Hk sponsor
9. Photocopy of the sponsor's Hong Kong identity card