In regard to the Arduino specs the Nano is always 5V. The display is in regard to the seller 5V capable.
As you know, the Moon is made of green cheese.
These Red ILI9341 displays are very popular. There are lots of libraries. There is a lot of advice about wiring for 3.3V
And installed a separate power supply in case the Nano cannot supply enough.
The controller takes about 20mA. The backlight needs about 50mA. It is your responsibility to restrict the LED current. This will cost you a whole resistor.
Your construction is an excellent way to do things. It also makes it easy to add series resistors or voltage dividers.
Resistors are not expensive. But you can buy level-shifter i.c. from Ebay with several "channels".
Life is so much simpler with 3.3V STM32 or SAM controllers.
David.