I know the answer is no but I have a thought experiment that seem to be violating that. Imagine two persons living on two different planets namely A and C which are 10 light years apart. There is a planet in between, B, which is located exactly at the same distance from A and C. If two persons from A and C get on their hypothetical spaceships at the same time, that can travel around .99C, and move towards B, they can talk to eachother in around 5 years. Didn't information just convey between two persons at the speed of ~2C in this case?
The principle is that information cannot move from Point 1 to Point 2 faster than the speed of light. In the example you give, information moves from the initial positions of the two participants to Planet B at less than the speed of light, so the principle is not violated.
The limit here is about how far the information can travel between two points. If people who originate at those points move while the message is propagating, that can reduce the time it takes for the people to get the message, of course, because it cuts the distance that the message has to travel to reach them. (But it does not reduce the minimum time necessary for the message to get all they way to where the people started the scenario.)
So in your case, the travelers from A and from C arrive at B in just over 5 years. No violation there as you specified they were traveling at $0.99c$. We're good to this point.
Upon arrival at B, the travelers can speak to each other essentially instantly. No problem here either because they are in the same location, so the information is traveling (approximately) 0 distance. Speed is not a factor.
Now if the traveler who started from A wants to relay a message back to his home world, he can do that. But his message will have to travel the 5 light-years between B and A, so that will take time. Exactly 5 years if he sends the message on a carrier that propagates at speed $c$. So a message relayed all the way from C to A by this process takes a bit more than 10 years, computed as a the bit more than 5 years it took the travelers to reach B from their respective home worlds and the 5 years it took for the relayed message to travel from B to A. That's consistent with the limit of 10 years that it would have taken if the message had been sent directly from C to A at the speed of light from the start. Still no violation.
A couple things to think about with thought experiments such as this. First, the notion that both individuals (from Planet A and Planet C) will get into their rocket ships at the same time is an easy thing to say, but not so easy to implement. There is no guarantee that watches in two different locations will be synchronized so even if there was some pre-determined time for when you would each start out your journey, the concept of let's start at the same time is not easily defined. Second, one needs to clearly define the frame from which time will be measured. If the notion is that I (as the traveler) will travel for 5 years from A to B and then be able to exchange information with an individual coming from C after experiencing only 5 years, then that is wrong. When I am traveling at speeds near c, my time duration becomes nearly zero. I can move from A to B at .99c and arrive at B experiencing essentially no time passage (that is I am the same age as when I left A). So, let's say I have a new grandchild on Planet C and they wish to convey this to me. If I stay on Planet A my grandchild will be 10 year's old when I learn of their birth (assuming the information was transmitted at the speed of light). If I jump on my spaceship (even though I have no way of knowing that I should do this) and travel at .99c to B, then my grandchild will be 5 years old when I learn of the birth and I will not have aged at all. In either case, the information never traveled at a rate faster than c. The point being, one needs to think through all aspects of their thought experiment.