You have a Virginia Creeper (Parthenocissus quinquefolia), a rapidly growing deciduous woody vine that can grow to 50 ft. New roots develop when the nodes of the vine touch the ground as well as from seeds. The vine has 5 leaflets and oval adhesive discs at the end of tendrils which adhere to walls and fences. Virginia creepers are often grown for their brilliant red fall colour. The following web site offers further information and photographs of this vine.
As the vine grows to its potential it can get quite heavy and may damage your fence and the roof of your shed. If you would like to get rid of it, you will have to be persistent. It is not easy to get rid of. Herbicides have been used in the past, but the Toronto Pesticide Bylaw would not permit the use of these in home gardens in the City of Toronto (as this would be considered a cosmetic use).
The best approach will be to cut the vine at it’s base, dig out the roots. As soon as new shoots appear, dig these up as well. Eventually the roots will die from lack of nutrients. You will have to be diligent. It is possible to get rid of this vine in this manner.
Enjoy your new garden!