Seemingly simple math and lightbulb problem

For convenience, let's designate four bulbs with the letters A, B, C and D, and the spare one - S. Now let's divide the life of one light bulb into four equal parts: 4,000 ÷ 4 = 1,000 hours. To get the most out of your bulbs, you need to replace them every 1,000 hours.

1. After the first 1,000 hours, the math should be replaced by a spare S. Now, until the end of its service life, light A will have 3,000 hours, light B 3,000 hours, light C 3,000 hours, light D 3,000 hours, light S 4,000 hours.

2. After 2,000 hours, the mathematician needs to return light bulb A to its original place, and light bulb S to replace light bulb B, which should be put into stock. Until the end of its life, light A will have 3,000 hours, light B 2,000 hours, light C 2,000 hours, light D 2,000 hours, light S 3,000 hours.

3. After 3000 hours, the mathematics should return light bulb B to its original place, replace light bulb S with light bulb C, and put the last one in stock. Until the end of its life, light A will have 2,000 hours, light B 2,000 hours, light C 1,000 hours, light D 1,000 hours, light S 2,000 hours.

4. After 4000 hours, mathematics needs to return light bulb C to its original place, light bulb S replace light bulb D, the last dispose of. Bulbs A, B, C and S have 1,000 hours remaining until the end of their service life.

After 5000 hours, the remaining bulbs will burn out.

Answer: 5,000 hours.