I don't know what can be done to solve the problem but offer these thoughts:
cat 5 is a cable with twisted pairs over which differential signals are transmitted with good drivers.
The DS18B20 or dht22 sensors use 1 wire technology where data from the sensor has
to be sampled by the Raspberry Pi at certain bit intervals. Ideally the data would have well defined
logic high and logic low voltage levels but the real life issue of cable capacitance and the pullup resistor
can degrade the signal, especially with a 75 foot cable. I would doubt that the dht22 has a signal driver
suitable for driving a cable of that length. The DS18B20 offers CRC to check data integrity.
I would mount the dht22 on a Rpi cobbler board and get it working. If possible use an oscilloscope
to view the data. Then splice in some cat 5 cable and observe the signal. A lot of work.