A US government bond matures in 10 years. Its quoted price is now 97.8, which means the buyer will pay $97.80 per $100 of the bond's face value. The bond pays 5% interest on its face value each year. If $10,000 (the face value) worth of these bonds is purchased now, what is the yield to the investor who holds the bonds for 10 years?

This is from an engineering economics course.

Here's the equation I came up with:

9780 = 10000 (P/F, i'%, 10) + 10000(.05)(P/A,i'%, 10)

I'm really not sure what to do, so I went with the guess and check method. I eventually figured out that i'% is going to be in between 5% and 6%. But after that, I don't know what to do.

5%: 10000(.6139) + 10000(.05)(7.7217) = 9999.85

6%: 10000(.5584) + 10000(.05)(7.3601) = 9264.05