In addition to the previous excellent advice re: 180ohms minimum, I notice you said LEDs plural. When powering things directly from Arduino pins you have to keep in mind two things:
The Atmega328 chip that powers most Arduinos is rated for no more than 200mA total current. The chip itself uses up to 40-50 mA, leaving you with 150, or no more than seven LEDs at maximum current.
If you’re using a small Arduino, like the Pro Mini or its numerous eBay clones (which I love), the onboard regulator (if you’re using it) may not even be able to produce the 200mA. So if you’re using an onboard regulator, check what the regulator is, and look up its maximum rating.
And an extra, keep in mind, that at high currents like anywhere near 20mA you won’t see the full 5V, there’ll be some drop in the internal circuitry. Maybe more like 4.5, plus or minus a bit. Shouldn’t actually matter for most purposes.
I rarely use the Arduino outputs for over 10ma to insure not dinging them. I make driver boards that will handle upwards to 500ma at up to 45 volts using seven channel driver chips. Three chips per expansion boards will handle all 20 usable outputs. At a bit over 75¢ per chip and a $1 for the board makes for a pretty cheap high current driver for the Arduino UNO.
And remember to really, really, really overdesign to avoid spikes if you’re working near the limits of these devices!
Remember why the old joke isn’t so funny: ‘How do I get maximum brightness out of an LED?’ “Crank up the voltage until you hear a pop, then turn it down a RCH and you’ve found the setting”
(we need to start a contest for 21st Century backronyms for certain precise measurement terms… [;)])
That’s the electronic equivvalent to how it was said Colin Chapman designed Lotus race cars - keep removing stuff to make it lighter, when something breaks, go back to the last version.
There will likely be little perceived difference between an LED running on the bleeding edge at 20ma and one running close at say 18ma, which gives a slight amount of headroom.
Something else to consider - there are LEDs, and there are LEDs - instead of ordering the cheapest Chinese ones on eBay, look for high efficiency red LEDs, if you really want bright. They can be blinding when run at half of their rated current, so running at 3/4 would amke them super bright yet not in danger of a slight voltage bump turning them into flash bulbs. Be sure to read the data sheet on the LEDs you use, the numbers tossed about are general rules of thumb and MAY be correct for the LEDs you use, but the right way is to be absolutely sure and get the information from the manufacturer or the seller.
To calculate the resistor, it’s (Source voltage - LED voltage) / current in amps = resistor value. Since resistors have tolerences, they don’t come in every possible number, so always pick the nearest HIGHER standard value.
And on top of that, if you want to go brighter still, consider LEDs with effective heatsinking, like those in full-scale headlight or home bulb replacement applications. I’m more familiar with these putting the die directly on something with high thermal conductivity instead of ‘potted’ in clear plastic, so you may wind up with something like SMDs mounted on the end of a stick of material which is then heat-sinked itself rather than ‘carving into’ a plastic one along the leads and adding thermal-transfer material there.