The time is shown to the nearest 5 minutes by illuminating characters on this grid:

TFOSNFIX
HWELEVEN
MURIGHTE
FTOHIRFO
TEWENTY5

Necessarily somewhat "idiosyncratic" words, for example, 4:35 is

.FO.....
.......
.UR.....
.T.HIR..
.....TY5

The hour and minutes are illuminated in different colours.

Jaycar sell a shield with an 8x5 matrix of RGB LEDs . This greatly simplified the project.
I created a laser-cutting design to cut and etch two sheets of thin black on white acrylic. One piece sits over the LEDs and the other sits on top, and the LEDs shine through the etched characters.

I thought I might need light-breaks between the characters so included some alternatives, but in fact there's really no bleed-through to adjacent cells.

The shield is perhaps a little odd in that it provides headers as though you could stack something on top.  I created a small "sidecar" board which plugs into the headers and holds the RTC, push-buttons and an LDR. It sits to the side of the shield.