Maybe because you don't print anything to the TFT? This is a hint, post your sketch. Also, please post a schematic / wiring diagram (a photo of a hand-drawn one is fine); it will make it a lot clearer compared to your description ( e.g. a Nano does not have a pin called LED so we don't know what you're talking about )
If your ST7735 is a 3.3V device, have you verified that its input pins can handle 5V?
I do not think.
I have a ST7735, which is for 5 volts (at least that's how it was announced). In practice, it turned out that it CAN be powered by 3.3 or 5 volt on Vcc pin, but the control pins should ALWAYS be at 3.3 volt levels. If you powered it with 3.3 volts and operated it with 5 volts, you may have burned out its driver. For me, the display worked normally with the Arduino Nano by feeding it with 5 volts and adding resistor dividers to the control pins to lower the levels from 5 volts to 3.3 volts. It is good to add what @sterretje advised you so that we have a better chance to help.