Controlling 5 - 10 RGB leds with Arduino Uno, simplest solution?

Hi, I know this is way simpler that some of the other questions on here, but I am quite a noob to electronics. I want to make an RGB led lamp, with 5 - 10 RGB leds, depending on whether there is a compromise on brightness or not. I would like it to be as bright as possible, and that's why I'm asking here, as I am quite the noob.

I intend to use a 74HC595, my RGB leds are common anode leds. The arduino is being powered with a 5V adapter plugged into a wall. Where can I look to learn what I need to be able to figure this out? Is there a tutorial or a set of tutorials I can follow, whereby at the end of it I will know what I need to be able to confidently se this up?

I have worked through a 74HC595 tutorial, and can set up leds using that, but it's the drop in brightness that I've seen others complaining about that concerns me.

note: I am coming from a programming background, and am unsure about how to work with the electronics considerations, but am comfortable coding what I need to when it's all set up.

Show us a good schematic of your circuit.
Show us a good image of your ‘actual’ wiring.
Give links to components.

The 74HC595 is limited in the current that it can handle. 70mA for the chip means less than 10mA per LED with them all lit. See the data sheet.

There are higher current shift registers for driving LEDs.
TPIC6B595PowerLogic 8-Bit Shift Register for instance.

Maybe your actual connection diagram is needed.

Controlling 5 - 10 RGB leds with Arduino Uno, simplest solution?

WS2812 or NeoPixels.

+1

Ah, you already have the LEDs.

Common anode was a good choice.

Are you wanting to mix any colour, or happy with the basic 7 (red, green, blue, yellow, cyan, magenta, white) ?

Because the TPIC6B595 suits driving common anode LEDs. The 74HC595 is not suitable for driving them with more than a few mA total.