KungFuPanda

(1) if you discout the 10 years annuity using ordinary annuity, you would have to deposit the money in the beginning of year 4 to get the money in year 5 (End of year payment). In other words, to recieve it in 5 years, you need to deposit the money in year 4. Year 4 is thus the year you need (x) amount.
(2) Another way to do it, is that since the first payment comes in year 5…  you can find PV using annuity due or beginning payment for 10 years. This gives your a PV of 27980.99. Changing back to End payment, then discounting back 5 years gives you the 18,186.
TVM is simple when you think in terms of timing and when you get the money. If you master timing, you master TVM!
Hope that helps