This is the problem
XYZ has 500,000 shares of common stock outstanding throughout 2004. In addition, the corporation has 5,000, 20 year, 7% bonds issued at par in 2002. Each $1,000 bond is convertible into 25 shares of common stock after 09/23/05. During 2004, the corporation earned $600,000 after deducting all expenses. The tax rate was 30%.
Compute the proper earnings per share

Do the dates look right to you- I was wondering if the 09/23/05 was a typo.
Any ideas on this one- diluted basic earnins per share, I really don't know

Yes, the 09/23/05 looks right to me.

Basic EPS would be (600,000 x .70) = 420,000 / 500,000 = $0.84 Net Income

Diluted EPS would be:
Basic 420,000 / 500,000 = 0.84

Bonds
Numerator - [600,000 + (5,000,000 x .07)] x .70 = 665,000
Denominator - (500,000 + 5,000x25) = 625,000
Bonds 665,000 / 625,000 = $1.06

Therefore, the bonds are anti-dilutive, so diluted EPS would be equal to basic in this case of $0.84