It sounds like you could have one of two problems.
1. You are exceeding the Ringer Equivalence Number REN
or
2. Faulty cabling.
1. The REN
In the United Kingdom, the maximum REN available to each telephone line is 4. This effectively restricts the maximum number of attached devices to 4.
Most simple devices like modems or telephones have a REN value of 1. It will be printed on the underside of the phone or in the spec’s in the case of a modem.
However, because in many cases devices actually have a REN value which is less than 1, this means that for practical purposes more than four items can be connected. This however is frowned on by the network operators because if too many devices are attached, the ring signal becomes unreliable, resulting in devices failing to ring.
Resolution: I would suggest you unplug one of your phones and see if the problem goes away. If it does you will just have to live with 5 phones. The only other way to fix the problems would be to install a small exchange, however even these have a REN for each line and can be expensive.
2. Faulty cabling.
Although unlikely I have seen a similar problem where someone had installed an extension under the carpet. Overtime the cable had become crushed and the insulation on the two cores had been damaged. This caused a short when the phone rang however the phone worked fine while you were talking on it. I would assume this has to do with the current (power) being carried. Electrical current will always find the easiest route to ground or neutral. When the rigging signal went down the line the current was strong enough the jump from one core to the other.
Resolution: Trial and error visually inspect all of your cabling for damage or bad connections.
Feel free to contact me at lelsweetman@hotmail.com if you want any further advice with this problem.
lel, April 2004