There's a thing called Penguin that, among other things, is supposed to find unnatural links and penalize sites for them. Unnatural links are links that are in one way or another under the control of the publisher who benefits from those links.
In statistical analyses there are signals and patterns that identify groups of links as unnatural.
Mix things up much more than you are doing, dont link to all 5 sites, watch the anchor text, dont give them precise generic instructions on what you want them to do - that creates footprints, let clients do things for themselves, you dont want 200 footer links appearing for example.
If you have to manage them then phone and suggest different linking ideas to them, be creative and take your time.
Your present strategy is an approaching train wreck.
I wouldn't touch this linking strategy with a 10 foot pole LOL. You are asking for trouble. As Graeme_p and Martinibuster pointed out, this is very unnatural and likely easily identified by Google's algorithm.