Using a relay switch to switch power to solenoid
There is no real difference between the 5V and 12V relays. It's mostly a convenience depending on the supply voltage you have. A 5V relay is more convenient for USB. This voltage refers to the switching/coil voltage.

The 15A 24V DC does mean that, it's the maximum switched load can be supported. If this is good for your solenoid depends on its current. If you don't know the inrush, assume 2 to 3 times the stated current. Your solenoid is 4.5 Watts, at 24 Volts means 180 mA typical. Rule of thumb rounding, assume 1 Amp for the power supply and relay supported load voltage.

Usb has a max of 16 feet without a hub or booster. Keep it near the computer, and extend the 24 Volt side, at 60 feet (120 round trip), with typical 18/2 AWG cable, you shouldn't see any significant voltage droop. The solenoid should still trigger at a lower voltage anyway.

Alternatively, think about using a remote relay. Wifi, or RF. Or ethernet. Or if you already have the USB relay, use a small computer to drive it. Something like the Raspberry Pi with a wifi usb stick or ethernet.