Let's say I'm a baker with 10 rolls. As I understand, every roll counts as a vote so I have 10 votes towards any proposal. If someone wants to delegate his 5 rolls to me in cycle N, when will his 5 rolls be counted towards to my votes? Would my votes count be the same as my baking roll count(10 rolls) at cycle N? Would that mean I have to wait until ~cycle N + 7 to have 15 votes?
The stake of each delegate is computed at the beginning of each voting period.
If a voting period starts at cycle n, your rolls are counted at the very end of cycle n-1 and that value is used for the whole period, that is up to cycle n+8.
Roll count towards voting is independent of roll count towards staking.
Look at this baker, for example: they had a large delegation (2 million + XTZ) that caused them to be overdelegated, and the delegator moved to another baker before cycle N + 7 came. But their vote was accounted for with 243 rolls, which will only be in effect for staking purposes in upcoming cycle 84