What are some skills I should be learning/practicing in preparation to take over as an E5 squad leader?

How to delegate to your team leaders
Time management.
Active listening
Communication skills. How to give orders in a clear concise manner. As well as receiving brief backs

How to properly counsel

A lot of the things you are wondering about learning have already been taught to you by virtue of listening and watching your squad leaders and team leaders received and give orders.

There are two distinct fundamentals of leadership and those often are confused by lots.

There’s a huge difference between being a leader and leadership.

Leader: a position granted by virtue of rank or assignment.

Leadership: an act or leading with compassion, care, and love for the job you do. Leadership is an art, a craft that must be hone and sharpen and applied different to different situations and people.

* Learn to actively listen to your subordinates

* learn to passively tackle issues while maintaining discipline and good order.

*learn to receive and give orders and never shy away from owning those orders you are giving even if they are shitty.

* learn to manage your time wisely and delegate as much of the work as possible to your subordinates. It’s not ditching your job because you made rank, it’s that you have other tasks to tackle.
* learn to respect your subordinate time and persona space as much as possible legal.

* finally, learn to counsel, read counseling, and most importantly incorporate your subordinates goals into monthly counseling as much as possible. If you rate E5/SGTs, learn to read and understand the EES system and ensure your subordinates also understand its purpose and usage. Good luck.

Read up DAPAM: 600-25 for NCOERs

A lot of great advice has been posted already but I spent the past 3 years rated in either an E6 or E7 slot as an E5 so I'll drop my advice.

The knowing your job, those under yours, and two ranks up still apply. This helps as if you will be delegating and leveraging the leadership of your team leaders. You should also know the job above yours for succession of command reasons as well as autonomy and being able to anticipate future tasks and missions that might come down and you'll be ahead of the power curve.

Understand some might look down at you regardless of your position simply because of your rank. Just like trying to get your SPC and SGT, bust your ass and show why you're in that position and the good peers and leaders will help you improve in your position.

Admin stuff. Get good at having an organized folder on your computer for your squad. It'll make life easier.

If you aren't already, try and ensure you're being developed and mentored by your PSG and 1SG. I'll add more as it comes to mind