An RRSP contribution of $5,000 sadly does not save you $5,000 in income tax. The RRSP is a deduction, so it reduces your income by $5,000 but the effect an RRSP has on your taxes payable depends on your tax bracket.
If you are in the 50% tax bracket then a $5,000 deduction saves you $2,500. If you make less than $10,000 a year, the $5,000 RRSP contribution will save you no tax, because you are not paying any tax on that level of income. You need to know your tax bracket in order to figure out how much an RRSP contribution is going to save you.
I do hear from people who think if they owe $5,000 in income tax, that a $5,000 contribution will take care of the tax. We have not yet reached the milestone in Canada where the tax rate is 100%.