Is there a way to see how many votes I have left for the day (prior to the 5 votes left warning)?
Your profile shows the number of votes you've cast today. This and other voting totals are tallied at the lower-right corner of the
summary tab, even though they're not shown in the
votes tab itself.
For example, this is what that looks like right now, for my meta user:
Subtract that number from 40, and that's how many votes you have left today.
Another way to see the votes remaining is hover the cursor over the down tick button on the name of a user.
It will show, how many votes the user has already given. Subtract this number from 40 if the votes on questions are 1:3 in ratio with answer. Subtract this from 30 otherwise. As this answer suggests.