If I put $5,000.00 into an IRA this year, about how much could I expect to save on my taxes assuming my income remains stagnant?

Depends.  A Roth IRA is not deductible.  A Traditional IRA can be deductible if your income allows it.   How much to would save depend on your income and your margional tax bracket.   If you are in the 20% tax bracket then a $5,000 deductions would result in  about $1,000 tax reduction.  ($5,000 x .20).