Conversion of GDP PPP International \$ 2005 into GDP PPP International \$ 2011
I do not know where you got the forecasts for GDP, but it is very likely they do not include a forecast on how PPPs are changing. As such, a computation of the rate of growth of GDP in 2005 PPP is a mreasure of real GDP growth.

Hence, what you want to do is to concatenate two series. For this, take the latest GDP level of each country from the World Bank series in 2011 prices, and extend it using the forecasted GDP growth rates in 2005 prices, calculated from your database of forecast. Naturally you only want to forecast GDP for the years that are missing in the World Bank database. The reliability of this exercise depends on how outdated the forecasts from the 2005 database are.