How alkaline is your soil? You're right - that's going to be the limiting factor, as there are scores of both perennials, annuals and small shrubs that will tolerate partial shade (4-5 hours of sun is quite a lot!). If it is pretty close to neutral (pH of 7.0-7.5) you should be OK for many plants but if much higher than that, you will be rather limited.

There are numerous lists of plants that prefer alkaline soil conditions online. Determine your pH and start there....once you have compiled a list of plants that will tolerate your soils, you can narrow it down to those that will tolerate shade :-)