To be clear, you can take more money out of your RRSP if you like, you just have to pay income tax on it. You can withdraw any or all money you deposit to an RSP at any time you choose, but when you take money out the bank will withhold taxes. The taxes are at various rates depending how much you take out. The final tax rate is determined when you file a tax return the following year, and may be higher, or lower than what the bank withheld and sent to CRA on the date of your withdrawal.
For example, a non-HBP withdrawal of $5,000 will incur a 10% withholding tax, so you net $4,500. Then, after the end of the year of the withdrawal, you will get a tax slip noting that 10% tax was paid on that income. If you are employed full-time, you will likely have to pay additional taxes, but, again, not until you actually file your tax return, which is due April 30.
As an example, let's say you take $5,000 out of an RRSP today, and net $4,500 after withholding taxes. Also, let's say your marginal tax rate is 20%. This means you will owe the CRA an additional $500 in taxes. However you won't have to declare and pay that tax until April 2016.