Halve the squash lengthwise and peel. Scoop out the seeds and cut into bite-size (1-inch) pieces.
In a wok, heat the oil over medium-high heat. Add the ginger and whole spices and stir-fry for a few seconds. Add the squash and stir-fry for a minute. Season with both soy sauces and stir-fry for another minute. Add the water and stir to combine. Cover with a wok lid and cook, stirring occasionally, until the squash is tender, 10 to 15 minutes. (Add more water if necessary to keep the squash from sticking to the sides of the wok.)
Once the squash is tender, remove the lid and season with the brown sugar and Chinese five-spice. Toss the squash with the seasonings and allow the sauce to thicken a bit, about another minute. Remove from the heat, toss in the cilantro and serve immediately.