Using your numbers to demonstrate it of 1 year EROEI. Let's say we make a starting investment for one year where we take 5% of the world's energy output to invest into new renewable power. After that year is over, we have capacity to generate 5% of the world's energy output per year, but we don't replace any of the existing fossil plants, but put it to work for new energy plants. So the second year we spend that energy on another 5% of renewable energy. Now we have capacity of 10% of the world's energy budget at start of year 1. If we continue doing this, we have 20% after the third year, 40% after the fourth, and 80% after the fifth. By the end of the sixth year, we can generate 160% of the energy demand of the world at start of year 1. We can now turn off the fossil fuel plants and enjoy a 60% increase in energy output, most likely more than the world has grown in that time.

Now you wonder, won't it cost tons of money to use all of this energy to build new plants? Sure it will, but that's already priced into things. That's what we have banks for.

Your fears are unfounded.