Well that's good news!! I will calculate all the correct values soon enough. My main worry is that the circuit simply won't work because I don't really understand circuits.
In this setup, if I have multiple LEDs on in a column, will the lights begin to dim?
I have thought of 2 more issues & I have some suggestions.
1. I can't see any bypass capacitors on your circuit. You will need a 100 uF electrolytic capacitor & three 100 nF ceramic capacitors (1 near the uC & trhe others near the SRs) across the 5 Volt supply line. You are likely to have some strange results if you don't include these.
2. I doubt whether the SR that sources the current for the LED columns will be able to supply enough current if you have more than a few LEDs switched on at a time. Check the SR data sheet. This partially answers your question re LED brightness.
I have 2 suggestions.
1. You can save your self a lot of wiring if you use 2 Darlington arrays in lieu of the transistors & their base resistors. See the data sheet attached. You will see in the DS that there are several versions - the ULN 2802, ULN 2803, etc. You need the ULN 2803. Note that these have the base resistors inside them. Do you intend to have more than one LED on in a Row ?
2. If I were you, I would start with a small array, say 4 X 4 initially in order to learn the ropes before you attempt the full size one.
The second issue re brightness is that you will need a power supply that can supply sufficient current for when the maximum number of LEDs are alight.
I'll have further suggestions once you answer my questions above. If anything is unclear, just ask.