There are 5 standard LEDs total.
Nope. Sorry. There is no such thing as a standard LED. You would need to look at each LED and determine what voltage it is designed to work with.
Of course, exactly how you are controlling the LED has a lot to do with answering your question. If you are powering the LEDs from the Attiny85 (not exactly an Arduino, is it?), you'd need one voltage/current source. If you are toggling transistors with the Attiny85, and powering the LEDs directly from the battery, the voltage/current needs might be different.
The ATtiny itself has some voltage and current requirements.
The life of the battery (minutes, hours, days, months, years) will have an impact on the choice of a battery.
You need to provide more details.