Q.what flowering evergreen would you recommend?
A very old Rhododendron was just discarded from the front of my house and now the spot is bare. There is direct sun so I should probably look for a different plant to replace it. The spot is about 3 feet wide, and I do not want anything that grows taller than 5 feet high and 4-5 feet wide. It is a small front yard. I prefer it be evergreen but it does not need to flower, although that would be nice.

I have found a few plants for you that fit the criteria you listed and will grow in your zone 7-8 garden.
Dwarf Gossy Abelia
Dwarf Escallonia
Euonymus
Hebe
Dwarf Holly
Dwarf Boxleaf Honeysuckle
There are many more but these were a few of my favorites.
Front Door Garden Design – Best Plants For Entryways
https://www.gardeningknowhow.com/special/.../plants-for-front-entrances.htm