30 year old system, lateral lines might be clogged with solids. They would need to be replaced in that case. Or could be plant roots if there are large bushes or trees near the lateral lines.
With clay soil the system will drain slowly under normal conditions (this is counteracted by having a larger drainfield to spread the water out over a larger area). If the soil is already wet from rain or snow melt then the system may not drain at all for a bit.
4 loads of laundry is probably too much water for a 500 gallon system in clay soil, on top of all the other water you used that day and the previous couple days.
Try not doing so much laundry at one time and spread it out over a week or so if possible. Don't do laundry or use a lot of water after rainfall or snowmelt, especially if there is ponded water out where the system is (flooding in the yard). Ponded water means the soil is saturated and any additional water added to it will not infiltrate or drain.
Do you have a high-efficiency washer or an older model? Older models will use more water. How large is your house in square footage and number of bedrooms? 500 gallon tanks were common decades ago, but most jurisdictions these days require a minimum 750 or 1000 gallon tank for new systems. Your system may be too small for your house. Some people have no problems with old systems, others do, it mostly depends on system condition and water usage. Was the septic system inspected before you bought the house?