I am finishing my basement. There are currently round ducts that come off my main duct and feed the floor vents on the first floor. To provide vents for the basement, can I tap off the round vents that run upstairs, so these would feed one vent on the first floor and one in the ceiling of the basement, or should I run a new 5" round duct from the main duct to where I want the vent in the basement. My concern is I don't want to mess up my heating of the first floor.

Are you just wanting to run one (only vent)?
If so it probably wouldn`t hurt you. Your furnace system was designed for the size of your house,and sometimes (most of the time ) they can`t handle adding on more rooms or vents. One new vent probably want hurt . But if you tie into another existing duct you will be taking away from that needed vent on your first floor,(less warm/cold air) will be coming out . I would add another duct to the trunkline for the extra vent needed,, a little more then what you asked for but don`t add the new duct off the end of the trunkline and try not to be directly across from another existing duct,that also could take away from the upstairs air pressure,, I hope this helps,, lte us know

Install a separate run with damper to your trunk, but not on the end. You may also want to add a return.

Thanks for the helpful replies. I will add to lines to the main trunk to feed the basement and not try to tap off the branch lines.