I am trying to create a circuit with multiple 5V logical control lines pulled down with 10K resistor.
Is the below circuit the right answer? I can't help but feel like this will create a short across all logic lines.
Your pull-down resistors are correctly connected. They don't cause short circuits between the logic lines because the common connection is held at a fixed voltage. Any current that flows through one of the resistors will end up on the ground wire and return to the power supply.
Notes: 'V' for volt. 'k' for kilo. ('K' is for kelvin.)