This is admittedly a tough one, but I'll give it a shot. The Five Dynasties and Ten Kingdoms refer to the period 905-960 CE. It is sandwiched between the Tang dynasty, which was culturally a high point in classical Chinese civilization, and the Song dynasty which was another high point which developed a number of advances. Perhaps the most notable thing we can say about this period in between was it was marked by considrable political strife and disunity (as the name of the era would suggest!).
That being said, it was around this period that at lead two important innovations occurred. Wood block printing had been developed centuires earlier, but around this time we have the first transition to a movable type for printing, used for the Buddhist scripture, the Diamond Sutra.
More notable is the first uses of gunpowder in battle. While it was likely invented earlier, it is first mentioned in texts in the 10th century, and is first used in battle with mixed results.
The Song dynasty that followed was a period of innovation and growth in classical China. The decades after the Five Dynasties and Ten Kingdoms were more prominent for invention and expansion of trade.
If on the other hand, you mean the Northern and Southern Dynasties period (420-589 CE) we have more accomplishments of note. I'll mention the main ones below:
1. Buddhism gained currency in China in this period. It was widely followed by the mid-6th century.
2. This was also a period when music, calligraphy, poetry, and painting developed in ancient China.
3. Architecturally, the pagoda was designed in this period.
4. It was also a period of development in medicine, astronomy and mathematics (for example, the value of pi was calculated to 9 decimal places).
Hope this helps!