Since we are finished at the end of the day,
it follows that the number of computers is divisible by 3 and 5. However, we do not know which multiple of 15 the number of computers is.
if we let $a$ be the number of days cleaning 3 computers at a time, and $b$ be the number of days cleaning 5 computers at a time, we see $a\equiv b+2 \pmod 7$, due to the number of days between Friday and Sunday.
$5b\equiv 3a\equiv 3(b+2) \pmod 7$, so rearranging gives $2b \equiv 6 \pmod 7$, or $b \equiv 3 \pmod 7$. That means 3 days and some weeks will pass since starting to clean computers 5 at a time. Hence, 3 days and some weeks before the end of Friday would be the start of Wednesday.
Without knowing the total number of computers, today is Wednesday.