I have many white flowering shrubs around my property, with no idea what they are! They produce woody stems that branch out like whips from the ground to form a kind of "weeping effect" The stems/stalks are dark brown/reddish. They produce offshoot stems with small dark green leaves that are pinnately compound. The flowers are small white clusters that are trumpet shaped. The bushes grow around 5 ft. I prune them back so they don't get too high. They could probably go 6ft. if I let them. The flowers bloom in summer and then turn brown in fall. But, they stay on the plant in their clusters, dead and brown. Our house was built in 1914 in Metter, GA, and I think a lot of the plants are old-fashioned. Maybe not that old! But surely pretty old and established.
I have a similar plant that weeps and produces a yellow flower, but the flowers fall and it's not as woody.