Finding additional function values of an odd-periodic function.

Question

I'm in a calc I class where I'm faced with the question:

Suppose that f(x) is an odd function, and periodic with period 10. If f(3) = 4, find f(7) + f(5).

Unfortunately, this is not talked about in our text, which says to me I already have this knowledge but can't seem to make sense of it.

I know that an odd function has the property f(-x) = -f(x), but how does that help if I don't know f(x)?

What I was able to find thus far has been tied to more complex ideas which I don't know and we have yet to cover. It said a function is periodic if f(x + T) = f(x). Is this going in the right direction, and if so how can go about dumbing it down a tad?

Any links to info, hints towards a direction, an explanation of the type of problem this is would be appreciated.

Answer 1

Hint: For what $x$ does $f(x)=f(x+10)=f(7)?$ For what $x$ does $f(x)=f(x+10)=f(5)?$ Once you have written these out, use the oddness and periodicity to find $f(7)$ and $f(5)$ - it should be quite straightforward.

Answer 2

Hint: You correctly translated "odd function". You know $f(3)$, so you know $f(-3)$ and similarly for any couple of opposite values of the argument of $f$.
Now, $f$ is periodic of period $10$, so $f(3)=f(3-10)=f(-7)$. But then...