Cat 5 should be fine. You could add a network switch
if you want to add more ethernet ports to your network.
Where I live the router is located next to the cable modem down stairs. So, I ran one Cat 5 Ethernet cable up to the attic of the second floor where I have a network switch. From the network switch Cat 5 cables run down to all the bedrooms. You need to consider how your house is wired. If the router is not near the central point for all the room ethernet cables you could run a Cat 5 cable from the router to the 'central ethernet point' and install a network switch there to feed to all the rooms.
As far as distance, Cat 5 ethernet should be good up to 100 meters, so 75 feet shouldn't be a problem. A network switch, in addition to adding more ethernet ports to your network, acts a signal source, so from a network switch you can go another 100 meters.