So, is this a reliable solution?
I presume that the coils are driven by a DC voltage. That DC voltage may be somehow connected to the Arduino's 5V supply - maybe it is the 5V supply, or maybe it's something like a 12V supply from which the Arduino's 5V is derived. A schematic would be very helpful for a diagnosis.If any of that is so, you'll need a suppression diode on each of the relay coils. The diode is connected directly across the coil, with the cathode connected to the positive terminal. When the coil is energized, the diode is reverse-biased, and doesn't conduct. When the coil is released, the diode conducts and dissipates the coil's inductive kick. Maybe you have those already; I can't tell from your post.
Anyhow, I think I solved the problem! I've found some ferrite cores and thought it wouldn't hurt trying them out.
I use a RC filter in series with relay contacts.R=100ohmC=100nf
Flyback diodes fix a different problem, not this one.It'd help if you told us what those wires were. The control signals? The load?That filter is not in series with the contacts.