Children the age of 3 can be trained to recognize dangerous vs acceptable vegetable foods. At age 3 they can be in kindergarten and learning. They can also learn to acquire berries, honey, and to recognize and harvest edible insects like ants.
Presuming 90% of their training is survival skills and we don't mind the occasional injury or death of children in training, around age 5 they have the mental capacity to learn making fire, using knives, knapping flint into tools like spears, etc. They can already learn to throw, they could learn to make and use atlatl and slings:
A slung rock can have the impact of a 45 caliber bullet; and an experienced slinger can hit a bullseye (or a forehead) from a hundred feet: it is an under-rated hunting weapon, far easier to construct than a bow, and can use projectiles easily found. Further, it does not require the muscular strength of drawing a bow; the slung stone can be less than an ounce and the strength is just that required to swing it in a circle a half dozen times.
Note that the world's youngest sharpshooter (with a gun) is only six: http://www.telegraph.co.uk/sport/olympics/shooting/6009319/Worlds-youngest-sharp-shooter-aged-six.html
I provide that as evidence of the skill level achievable by seven-year-olds if they are trained.
I presume the children will be able to hunt small game (birds, squirrels) or even deer; will have (in class) butchered and cleaned these, and will know how to make fires and cook both the animals, and the vegetables they find.
Also, note six-year-olds are already playing baseball, they can be taught to use basic clubs, and presumably in training have already killed and eaten animals.
Likewise, they can be taught to build shelters (IRL they are already building themselves forts), find water.
On a coastline or river or stream, they could build nets to fish, or make basic fence traps: Sticks sharpened and hammered into a stream bed in a 'comb' pattern, to divert larger fish (those that won't fit between the sticks) into a longish channel that ends near one of the banks in a pen, or net. Rocks can be used, but you want the fence tall enough that fish can't jump it. My point here is you don't need hooks or knives or anything else; if necessary a stick can be sharpened by grinding it against natural rock, and some vines are suitable for tying into knots to make a basic net that lasts long enough to catch some food.
I don't think survival would be an issue for trained 7-year-olds; other than injury from falls and some predation and illness (viruses, infections).
To me the bigger problem is political organization; how they are supposed to cooperate. You will also have the problem, in about four years, of impending puberty and gender separation: In actual grade schools in the USA, fifth grade is the year (just before actual puberty for most) that girls and boys start separating themselves by gender; that boys start "showing off" and becoming aggressive and girls start whispering cliques. By sixth grade, gender issues are so rampant they routinely disrupt both classes and learning.
So in year 5, how your (now 12-year-old) children manage to deal with puberty, sexuality, the violence of competitiveness, rape, etc will be interesting to see (and hard to keep plausible and realistic).
That is what could kill them by droves, indirectly. The solution for chimps and gorillas is a combination of fight and flight: Some young males are disabled or killed challenging an alpha male; other young males exile themselves (and sometimes get a young female to go with them), but there is a low chance of that resulting in a new tribe.
In humans, the males will fight for mates (and the resources to attract a mate and support a family) and kill each other over it; in hunter-gatherer tribes, warfare between neighbors can be frequent and lethal, in fact the chances of being killed by another human can be far greater than the chances of being killed by the jungle!
That's the big problem. For these kids, survival may depend on tribal socialism (our natural state) in which everybody contributes to the community stew pot, sharing the results of their hunt and gather, helping to build common shelters and fires, tool making, etc.
When sexuality enters the scene, without any culture (taught and enforced by adults) to put restrictions on how to transform from a child into an adult sexualized person, a mother or father: That new twist (for them) could break up successful tribes into factions. The sharing stops and the parts become less than the whole: They may all die out.
I am also not so sure any of that could be taught to seven-year-olds before dropping them off, or if they would care, five years later. That would seem like a lifetime to them without any adults, and with no punishment or admonishment of anybody.