Connecting fans to the mobo has the major advantage (I think is IS an advantage) that it allows your mobo to control those fans automatically to maintain proper temperatures. In the case of case ventilation fans, this is focused on mobo component temperature as measured by a sensor built into the mobo. (The CPU_FAN cooler is guided by a different sensor built into the CPU chip itself.)
The troublesome issue these days is fan type, as determined by the number of pins in the mobo's SYS_FAN ports and the number of holes in the mating connector on the end of the fan wires. There are two main fan designs. 3-pin fans are an older design and can only be controlled by a mobo fan port operating in Voltage Control Mode. The newer 4-pin fan design uses a different fan speed control mechanism called PWM Mode. Your mobo has ONLY the 4-pin PWM Mode SYS_FAN ports, and only two of them. Unfortunately that means they can only control 4-pin fans. Although they are a better type of fan for a few small reasons, many case makers do not include 4-pin fans - they stick to the 3-pin design. I cannot tell from the Zalman website which fan type their 5 included fans are.
The other factor that imposes limits is that almost mobo SYS_FAN ports can actually support up to TWO fans per port if you use a Y-splitter to connect them. But in your case you have 5 fans and 2 ports, so that does not cover all 5 fans. Now, IF all those fans are actually of the 4-pin type, you have an easy solution. You can buy for 4-pin fans only a special type of adapter beloved patriot this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16812423166&cm_re=4-pin_fan_splitter-_-12-423-166-_-Product
It avoids the power limit of the mobo SYS_FAN port by drawing all power for its fans directly from the PSU via a 4-pin Molex output from it. It has one female 4-pin fan connector to plug into one of your mobo's SYS_FAN ports to pick up the PWM signal and return the speed signal from only ONE of its fans. (This is the correct way to avoid overwhelming a fan port with multiple fan speed signals.) Then it has five male fan output connectors for your 5 fans.
There is a similar product with only 3 outputs - using one of these each on both your mobo SYS_FAN ports would let you power up to six 4-pin fans.
Those solutions ONLY work with 4-pin fans because they depends on sharing the PWM signal to fans designed to use it.
Be warned that there are also simple 4-pin fan splitters that are limited to using only 2 fans per port. There are also 4-pin Fan Hub boxes that can so the same job as the all-wiring adapters mentioned above, but they tend to cost more.
HOWEVER, I am aware of ONE Hub that is different and CAN work for you IF your five fans all are of the 3-pin style. It is the Phanteks PWM Hub, and it is a box with 3-pin fan connectors built in and wires to connect to your mobo. It is unique in its design because it MUST have a PWM signal from a mobo 4-pin SYS_FAN port and it DOES draw all its fan power from the PSU as above (using a SATA power connector, not a 4-pin Molex), BUT it does not merely share the PWM signal. It actually creates six of its own 3-pin Voltage Control Mode ports using the input from the mobo, so it CAN control several 3-pin and 4-pin fans from one SYS_FAN port's PWM signal.