Do you have any advice on going from E4 to E5?

There have so many answers to your question I can hardly add to them. In fact it took me from 1976 to 2002 to make it to the rank of Sergeant and the pay grade E-5.
While have no secrets to being promoted quickly I do have a few others. One of which is that life is a journey, not a destination. Try not to let yourself get so wrapped up in the destination (fast promotions) that you miss the journey.
Just be yourself, be a good soldier, be proud that you you did your duty, regardless of what rank you happen to be. Above all make sure you never put your own personal advancement above taking time to help a junior soldier who might be looking to you for proper guidance. Good luck and thank you for your service to our great Nation.

Keep pushing to go to the board but you have to understand they don't just promote because your good at your job. You have to show that you have the potential to hold the next level of responsibility as well. I was in the same situation a couple months ago

That's the price you pay for being a E4 but if you're motivated and you are a good leader it is seen that E5 that is stealing your thunder well thats part of his job and if he's evaluating you then what you don't see is still shining because good leaders give good soldiers good evaluation so be patient and wait for your day

Stay motivated and volunteer for soldier of the quarter, year, etc. work on maxing out you PT, fill out a 4187 to go to Airborne School, Air Assault... These schools in combination with knowledge about Army policies will look good on paper the command will see you're serious more than other to better yourself. Oh and a key one is make sure you complete your SSD1, without it you can't go to WLC or even be considered for advancement.

Specialist.
You have to remember the most important thing now you're an NCO. And this was told to me when I made E-5. Everyone under you is more important than you.
Treat people with respect, and they'll respect you. Treat people like shit, and you won't be a good NCO. Don't be condescending towards people, remember these are the same soldiers who want to make their way to being an NCO as well. Show them what a good NCO does

Make sure that you have completed your SSD 1 for your level. See if you can get any other school (i.e. Ranger, Airborne, Air Assault). Read up on your Skill Level 1 and 2 tasks. This will put you in a better position for when you do get promoted, and it may put you above the other Sergeants that have been in the position for a while. Lastly, go to Soldier of the Month boards. That will prepare you for the promotion board itself.

Read the NCO Creed and heed its words. Develop your subordinates and lead them. Dont just manage them. True leadership is influencing and motivating. Every sentence in the NCO Creed is there for a reason. Go to the Soldier of the Month board and help your peers and subordinates to go and win. Discuss this with whoever does your counseling. Track your tig and tis and know exactly when you are eligible either primary or secondary. Most of all stay motivatdd and be patient.

become an expert in something, like hanging out with the mechanics to learn the little tricks of the vehicles, or commo, or armorers, or something, when you can get the equipment up again without having to call for support, you will be noticed in a good way

Be knowledgeable on everything. Your Soldiers will expect you to know everything.

Have you even tried teaching classes about your mos to the rest of E4 or Lower. Like that It will show your first line that you do have the potential of being a Leader because you can teach what you know