They seem to have dropping resistors for each LED. 2000 ohms (I'm assuming) with a 12V supply will give each LED approximately 6mA (a bit less depending on LED voltage drop). Not all that much. Without a schematic, hard to say for sure.
These LEDs could be designed for a higher voltage, like 14V (like a running car), or even 24V.
Best to put each one on a variable power supply, and measure the current. Most LEDs don't need more than 10-15mA each for full brightness.
If everything seems ok with 12V, your 200mA power adapter may be fine provided the total load is 200mA or less (40mA maximum per strand for 5 strands). Be aware that many of the cheaper power supplies give off a higher voltage under low loads. Some 12V supplies (wall plug types) may give as high as 18-20V with no load or little load. Measure the voltages of your supply first...