Posted replies show a varying amount of understanding of how tel_cum _ADSL works.
May I clarify please?
A telephone audio signal has a max frequency of 5kHz - technically also a low frequency signal. The two signals are combined and fed into the telephone cable to your house at the exchange. Sometime c.1990 it was found that a signal combined in this way was good for 1 to 3 miles from the exchange. Hence ADSL internet services.
So you only require ordinary telephone cable to extend the phone system (with or without ADSL) within your house. 'External' grade cable is only different in that it is more rugged & weather proof: unlikely to offer any advantage over internal grade for your 10m run (but don't run it thru water). An extra 10m run is nowt.
You can extend your existing cables by any jointing system you like. Common sense suggests making sure the existing connection to the exchange & any of your equipment which might be sensitive to static is isolated first. You can use IDC connectors, special tel junction boxes with internal screw terminals, simple soldering or anything else which gives a good connection. Thing to remember here is that it is all low frequency work, so just as long as connections are sound and permanent (& properly insulated) almost anything goes. Perhaps beware of dry solder joints, especially if the cable may be exposed to fluctuating temperature.
If you connect a phone directly to an ADSL enabled line you will hear much high pitched interference. A microfilter (what you are calling a "telephone/ADSL splitter") is in fact a low pass filter which just passes the telephone sound signal to your phone. It rejects the ADSL signal which is left untouched. Done this way you need a microfilter for each phone. The full telephone signal (ADSL+tel sound) is fed into your computer network card (which contains a high pass filter to capture the ADSL signal only).
Instead of multiple microfilters - which can degrade telephone sound if used en masse - it is better quality wise to use a dedicated filter at the point of entry into the house & have 2 internal circuits. One for the telephones & the other for the ADSL connection: suitable kit at
Simple routers usually offer a choice of connecting to each computer by WiFi or by an ethernet cable connection which can handle the higher frequency. It is ONLY for the latter use that you require Cat5 (or Cat6) cable. Cat5 cable contains 4 twisted pairs of wires within a polythene sheath. Cat5 cable construction is designed to limit interference between adjacent signals. (In fact only 2 pairs are needed for one ethernet connection, so it is possible for 2 computers to share one suitably terminated Cat5 cable.)
ie Cat5 cable is ONLY needed for the Ethernet side of a router because of the higher signal frequencies involved. Cat5 could be used instead of standard telephone cable - there is no advantage, but a huge cost disadvantage.
HTH