I do not have a cable run that long but here is the maths which may help you. This is for the power requirements only
Cat 5e UTP DC resistance is 28.6 Ohms per 1000'
Your distance is 25' Nest Cam power cable + 70' extension.
In the following scenario I am assuming that the Nest Cam power cable has the same resistance rating as the Cat 5e cable. Cat 5e is 24 AWG. If the Nest cam cable uses thinner gauge wires there may be a slightly higher voltage drop due to the increased resistance but given the short distance it will only be very small
Total distance = 190' (25+70 x 2) The x 2 is the return or loop distance, Only using 2 wires in the cable
Total resistance of wiring : 28.6/1000 x 190 =5.434 Ohms
Power requirements of camera is 5V DC 1.0A (1000mA) According to Nest Cam specifications here
Voltage drop over cable at 1.0A (1000mA) (Ohms Law E =IR) =5.434V
Therefore Supply Voltage required is 5V + 5.434V = 10.434V
Here is a power adapter 10.5V DC 1500mA that should be suitable for your requirements. Ensure that the polarity is correct when you connect it up.
If you use all 8 wires in the Cat 5e cable i.e. 4 for the battery +ve and 4 for the ground(Earth ) because they are all in parallel (4 battery wires are in parallel with each other and 4 earth wires are in parallel with each other), the resistance will be reduced to 1.3585 Ohms
Therefore new scenario will be:
Total distance = 190' (25+70 x 2)
Total resistance of wiring : 28.6/1000 x 190/4 =1.3585 Ohms
Power requirements of camera is 5V DC 1.0A (1000mA)
Voltage drop over cable at 1.0A (1000mA) (Ohms Law E =IR) =1.3585V
Therefore Supply Voltage required is 5V + 1.3585V = 6.3585V
The same power adapter in the link above will probably work OK when the 6V DC option is selected
Hopefully this is of some help.
Been reconsidering my statement that it will probably work OK on 6V with 8 wires in use. It may be that the voltage available to the camera (approx 4.6V after cable losses) will not allow it to operate at optimum level. Therefore I suggest that you use a 4 wire connection, 2 wires for battery, 2 wires for earth, and select the 7.5V option on the power supply. This will give you approx 4.8V for the camera which is closer to the 5V required. If neither of these work well use the 2 wire option at 10.5V this will give you the full 5V necessary. It will be by trial and error I think as the optimum voltage operating range of the camera is unknown, to me anyway.
"Hint" If you use the 2 or 4 wire option use only the coloured wires in the cable as that way it avoids confusion whether you have the correct wires connected at each end than if you use the whites as well.