For every $10,000 income ...
Yearly Spending: $5000
Yearly Savings: $5000
Interest: 5%
This looks nice and all, but you ignored inflation, which is a very important factor here. Assuming inflation at 2.5%, your interest effectively goes down from 5% to 2.5%, resulting in this:
Year Spending Interest Total Savings
1 $5,000.00 $0.00 $5,000.00
2 $5,000.00 $125.00 $10,125.00
3 $5,000.00 $253.13 $15,378.13
4 $5,000.00 $384.45 $20,762.58
5 $5,000.00 $519.06 $26,281.64
6 $5,000.00 $657.04 $31,938.68
7 $5,000.00 $798.47 $37,737.15
8 $5,000.00 $943.43 $43,680.58
9 $5,000.00 $1,092.01 $49,772.59
10 $5,000.00 $1,244.31 $56,016.91
11 $5,000.00 $1,400.42 $62,417.33
12 $5,000.00 $1,560.43 $68,977.76
13 $5,000.00 $1,724.44 $75,702.21
14 $5,000.00 $1,892.56 $82,594.76
15 $5,000.00 $2,064.87 $89,659.63
16 $5,000.00 $2,241.49 $96,901.12
With median income for US of ~$45k (quick google search), that gives $10,087 annual interest, so less than half of what you need to maintain the same, frugal (dis)comfort of life, unless you manage to get better yield for your savings.