Well, there are a
whole lot of problems here!
From your description, you are attaching the IR LED between two port pins. This immediately tends to limit the current which would be a somewhat good thing given that you have omitted the
obligatory current limiting resistor.
The
description of the KY-005 module is somewhat unhelpful as it incorrectly suggests both that the module requires a 5 V connection - which it does not - and that it is acceptable to connect it without the series resistor which it does not include. It might be expected to connect to a "servo" spill such as on various headers with a 3-wire servo cable which would be practical
if the board actually provided for a series resistor.
I do not have a series resistor in my circuit. Is that a standard value per LED?
No, not really though you might use rule-of-thumb values for each LED colour. For an IR LED with 1.5 V drop and 25 mA as being a practical current to be supplied by the Arduino, the drop across the resistor would be 5 V minus 1.5 or 3.5 V, and at 25 mA (which is an allowable current for the ATmega chip), a 150 Ohm resistor would suit.
In fact, with an effective 50 Ohm internal resistance of the chip drivers, a 120 Ohm resistor would be quite satisfactory. (Note that it is acceptable to include the internal resistance in the calculation
as long as the resultant current is correct.)