Your wiring diagram is correct, as (per the Sainsmart.com website you linked) the specs of the device are:
Input control signal voltage:
0V - 0.5V Low stage (SSR is OFF),
0.5V – 2.5V (unknown state).
2.5V - 20V High state (SSR is ON).
The Raspberry Pi uses 3V3 signals on its GPIO pins; a voltage level which is high enough to trigger the High State in the relay as per the specs. An Arduino (for which the same board is used) uses 5V signals on its GPIO pins and works equally fine with this board. The other circuitry on the board needs to be powered by a 5V source, for which you have correctly wired the board to the 5V power supply pin on the GPIO header.
The specs you quote are not completely correct, however. The GPIO header consists of power supply pins (1x 3V3 and 2x5V), several Ground pins, as well as GPIO pins. The GPIO pins (like GPIO17 you mention) are severely limited in the current they can supply (unlike the 5V pins which can supply at least 0.5A if not more depending on the rPi model). Each pin can output a maximum of 16mA (not 50mA as you mention), with a total maximum combined current across all pins of 50mA. This is enough to drive a few LEDs, but not much more. The pins are typically used for sending signals to other devices, and your relay is a perfect example.
As I mentioned, your circuit will work fine as you drew it (provided you supply a different power source to the relay terminals, the Sainsmart page says this about the Relay voltage and current it supports:
SSR Output (each channel):
Load voltage range: 75 to 264V AC (50/60Hz).
Load current: 0.1 to 2 AMP.
). It is common practice to put at least a resistor on the line between GPIO17 and the relay (1kOhm should be enough) to avoid a short circuit from frying your rPi via the GPIO pin. Also, if you want to be extremely safe, you can prevent an accidental miswiring from sending current to your output GPIO17 by wiring in a diode (make sure the polarity is right on the diode!).
Finally, since you are new to this, be extremely careful how you tap into the GPIO pins, especially the 5V pin. If you use proper female jumper wires there should be no issue, but if you decide to work with stripped wire on the GPIO end, you might end up inadvertently connecting the 5V pin with a GPIO pin, which leads to disaster (As I call it - "fried Pi"). Then - set your GPIO pin to be "output" (in whatever language/library you are using), and engage the builtin pull-down register (to make sure that when the signal "floats" it gets pulled down to 0V and doesn't accidentally trigger the relay).
PS: The video on the Sainsmart page is not much help, the only useful thing to observe is that in the demo they have the relay powered from a separate 5V supply instead of using the rPi's 5V GPIO pin. According to the specs, the board will only use 160mA, which is well below what the rPi can supply. So you're good either way. The Sainsmart page also has a Raspberry Pi "document" linked, but that page (https://github.com/fixedd/RPi_Relay_Interface#readme) has a disclaimer saying that its instructions are unnecessary for the Sainsmart module, as (quoting):
Note / Warning
This was formerly stated to be for the SainSmart relay modules, but it
was later pointed out to me that these boards actually already have
this logic built in to them.