I think Cytron did share about this in one of their article, the robot magazine, but cannot remember which version.
According to the author, the backlight can be directly connected with 5V, but the current consumption is quite high and will further increase the load of the 5V regulator, end up? Your 7805 is hot
. The author share the method of controlling the backlight using PWM via a NPN transistor. With this configuration, you can control the brightness from the microcontroller and further control the current consumption.
And normally you don need such high density light to look at the character on LCD. You can try the value on SK40C's schematic, I just apply what is being use by Cytron and it work fine for me, if I am not mistaken is around 50 Ohm.