Yes. It will keep your mind active however for how long is the question.

Too many nights of 4 hour or even 5 hours sleep, will slowly degrade your physical and mental health. Aside from the obvious fatigue, you will also suffer short term effects like inability to focus properly, being more irritable, memory implications and difficulty maintaining a train of thought.

Long term effects are even more severe, and can range from mental issues like depression and severe paranoia, to physical issues like diabetes, dementia and heart failure.

Ideally you would want to get at least 8 hours of good quality sleep every night. In the worst case scenario, you should at least be getting 7 hours.

It is the cool and trendy thing among many, especially young people nowadays, to brag about how little sleep they can get away with. The truth of the matter is, the people that can get away with just 4 hours of sleep every night are usually "natural short sleepers", meaning they were born with a gene mutation which, by altering their sleep homeostasis, allows them to sleep less but recover as much as a person sleeping for 9-12 hours. People without this gene that are only getting 4 or 5 hours of sleep a day over a prolonged period, will despite their bravado, become inevitably plagued with many of the issues mentioned earlier (depression, loss of brain cells, diabetes, heart failure and so on)

(Read the research here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2884988/)

My recommendation? Go for at least 7 hours of sleep a day if possible. If you don't have enough time to sleep for a continuous 7, then just sleep for as long as you can and make up for the sleep you missed out on, by taking naps throughout the day. Even just two or three quick 30-minute naps every day will go a long way in providing recovery time for your body and brain.