SN74LS07: SN74LS07 description

For bipolar devices (TTL, LS), an open input will be read as high, but it floats near the switching threshold, so it can be easily affected by noise. For CMOS devices, an open input will float anywhere, which can make the device oscillate, or damage it (see [FAQ] How does a slow or floating input affect a CMOS device?).

So unused inputs must always be tied to V_CC or ground. (With bipolar devices, high level uses less power; with CMOS devices, it does not matter.)

To shift the voltage from 3.3 V up to 5 V, use a CMOS device with TTL-compatible inputs, i.e., SN74AHCT04.

The SN74LS07 has open-collector outputs, i.e., when the input is high (or unconnected), the output is high impedance, and does not have any specific voltage; what you measure are side effects of your multimeter's circuitry.