There's this lovely shrub near my pool, about 7 feet high. It has flowers in clusters, like hydrangeas or lilacs. They vary from pale pink to pale green. And though I chose a poor (slightly deformed?) example when I picked one for a picture, it definitely has 4 petals per flower, not 5. You can tell if you look closely. And many of the larger leaves had 5 lobes, if that helps. So far I've seen it blooming in June/July.

Can you post a photo of the plant itself?

Oak leaved hydrangea leaves, Hydrangea quercifolia may be?

The sterile flower shown points to hydrangea or viburnum.

I googled hydrangea quercifolia, and I think that's it. Thank you all!

Looks like a Hydrangea to me.

Alice is a tall oakleaf hydrangea that is commonly sold almost everywhere. But there are other tall ones like Snow Queen and Snowflake (double blooms).