The thumb can be treated as a finger but mostly within the context of fingers. Both digits and fingers are hypernyms of the word thumb. Here are my dictionary* definitions:
the short, thick first digit of the human hand, set lower and apart from the other four and opposable to them.
each of the four slender jointed parts attached to either hand (or five, if the thumb is included)
a finger (including the thumb) or toe
Thus, saying you have
5 fingers on [your] left hand is not wrong but some may consider it awkward, since there is really nothing special about having five digits on either hand! Indeed, it is acceptable to treat the thumb as a finger, as I earlier alluded to, and I give a few examples to illustrate:
- Count on your fingers.
- He rubbed his fingers vigorously.
- Show me your fingers!
- Your fingernails are dirty.
- All my fingers are cold.
- How many fingers am I holding up on my hands?
- 'Which finger did it bite?' 'It bit my THUMB!'
- Her fingers flew nimbly across the keyboard.
- Have a look at the fingering chart.
- He fingered the steaming mug gingerly, taking quick sips in between mouthfuls of bread.
However, one would rarely, if ever, hear finger used in a singular sense to directly mean thumb. Digit[s] is rarely used in everyday conversation, and since it also includes toes, one is probably most likely going to hear/use fingers when the manual digits are involved.
*New Oxford American Dictionary, 2nd Edition