Going to hazard a guess in that when you say 'use 5 colors' you do mean like red and variants, blue and variants and not just 5 colors that are the same color-hex i.e #D20103 for your red and ONLY that color for your red and #060270 for your blue and ONLY that color for your blue - up to 5 variants?
Even if one were to be making an 8bit game such as the OG Super Mario Bros on the NES, that game had a possible 256 colors to choose from and whilst not using the entire palette it would technically use way more than 5 colors.
For the record my game is going to use 3 - White, Black and Grey. But if we go by the hex system there are technically more than 5 colors in there because of the differing shades of each one.
Sorry to bug you with this and ramble on but it is a question I myself was going to ask you as the host Mana, but thankfully Thoughtful has brought it to light since originally I was too lazy to do so myself :)