Diesel fuel does not directly harm the materials and equipment in a petrol engine, but adding diesel to petrol will dramatically lower the octane rating.
Diesel fuel has a cetane rating which is functionally the opposite of octane rating. Pure diesel fuel has an octane rating somewhere between 25 and 40. Petrol sold at the pump runs from the upper 80s to lower 90s. (Generally 91 or higher in the UK, 87 or higher in the USA.) Each 2% of diesel added to petrol lowers the octane rating of the mix by about 1 point. So if you really have 10% diesel in the petrol, the octane rating has been lowered by about 5 points. But remember that a fuel gauge that reads empty is usually lying, and there's more fuel remaining in the tank than indicated. What if the mix is really 20% diesel? Octane would be reduced by 10 points.
If you fill your tank with this stuff, it will run like sh.... uh, it will run poorly. The engine will knock. Although all modern petrol cars have a knock sensor to deal with variations in octane rating by altering the timing, a drop of 5 to 10 points is really too much for the ECU to deal with, and it's possible for excessive knock to damage the engine. This is especially true of you have a high performance, high-compression engine that requires high octane fuel to run at peak performance.
In my opinion, your proposal to mix 5 liters of diesel-contaminated fuel with 30 liters of pure petrol per week is a reasonable approach that will greatly reduce the likelihood of adverse effects, especially if you buy the highest octane petrol available during this period. It may be costly, but certainly less costly than paying a company to dispose of the contaminated fuel.