A rally to $5k is possible for Ethereum, but to be certain we need Bitcoin to get closer to the $64k ATH it established in May.
September is usually a bearish month for Bitcoin, so I don't expect Ethereum to have a breakout in value, even though ETH is burned every day.
The current high transaction fees in Ethereum are due to the high level of NFT transactions. It's like the DEFI wave in previous months.
That's clearly possible because the highest ETH price in May this year was also close to $5K, even though at that time there was no burning program on ETH, so it's definitely very likely if Bitcoin can approach $60K again this month or by the end of the year.