I have a team member that, no matter the situation, leaves at 5:00pm every day. Should I look to replace this person?

You have a volatile situation. When you accept a salary position you are expected to put in the extra time at work when the need is there. There is no bell ringing at 5pm that you are done for the day. There is nothing wrong with going home at 5pm if you are done for the day and your support is not needed.

It's better to cut this person off right now to cut your loss and replace that person.

This is interesting. However, from your narration it seems you work in a matrix kind of structure where you have no full control over your team members. Salaried employees have terms of reference such as reporting times and departure. These are the times they “sell” to the organization in exchange for their salary. So if he reports on time and leaves at 5Pm daily as you have stated, he is within his employment terms of reference.Beyond that would be working overtime really which should be avoided.
That being the case, I would suggest that you inform him of all the work he needs to undertake beforehand and agree on the timelines for delivery of the same so that it doesn’t impact other activities that the team is handling. The same should go for the entire team. However, if all fails you or the team should not be held hostage as no one has a monopoly of skills.

Hi Bruce - I would suggest you to set your expectations right with your team member. Inform that team member that when there is a pressing need, business may expect him to complete the work prior to leaving the office. Maybe you could give him time off for extra work (since he is salaried and if your organization has comp off). It could also be possible that he has other commitments after office hours (maybe sick family member to attend to or have part time job, etc.). For example, we have a team member on our team whose has set his expectations very straight. He would be in office by 6:30 AM, but he has to leave work at 3:00 PM to spend time with his kid. Apart from the salary, he is not expecting anything else (like growth or promotions).
You may consider option to provide him infrastructure to allow him to work from home when there is pressing need - like providing him a laptop(?)
Give your situation to him and try to find out what are his constraints. Alternatively, you can plan for work and give him heads-up in advance. Normally, I have seen at few projects that 'urgent' work tend to show up always at 5:00 PM when we are about to leave for work. When we dig deeper into this the symptoms would have started to show up 2 or 3 days ago, but when it falls on your lap it would be late evening and its already bumped up in priority. Favorite time to bump up is on Fri 5:00 PM. If this is the norm, then the problem may not lie with your team member, rather the person(s) reporting the problem. You may have to set a process where any problems reported beyond X PM will be dealt the following business day (unless its stopping business completely). When this expectation is set, business will try to be more proactive.
Hope this helps.

Problem is a gap between perceived reality and desire reality. You can work on perception, you can work on desire or you can work in the gap. People always behave in a way for a reason. If I would in your situation (I was lot of times including today) I will work on that. I always tried to not replace people.

Similar views as Sachin.

Empathy. Understand what more about this individual, the hidden side. Maybe his wife has a night job and he needs to get home for the kids. Maybe his kids have activities to go to. Maybe he has a sick parent he is caring for and needs to relieve the nurse.

Or, not. But go into a discussion with empathy to understand more about the other aspects of this individual.

From there you can work to find a common ground. Read what Sergio wrote. It's a bit scientific, but it is accurate. Don't let negative emotion skew your perception.

Agree with Sergio.

There is a gap in expectations from you, him, and others. Which is normally a good thing, coming from diversity and mutual respect is needed to close the gap. Your team rules should set expectations, they are not set in stone and not sacrosanct, you can and should adapt to situations like this.

A leader takes the resources available and builds a team from them.

For me this person seems to be the expert at hand for a dedicated skillset missing elsewhere within your team structure. Furthermore, I understand that the overall working attitude is mostly disliked by the other team members.
This seems to be the perfect match for outsourcing the task.
Propose to the person that there is no need to be a team player with the others, if this is desired by you and/or the person.
Or try to communicate that for you it is ok if the person stays outside the circle of actively involved team members, but the perosn needs to work on the relationship with the other team members. E.g. giving colleagues the understanding why the person needs to leave at a regular schedule and why it is important to do this steadily.
Bottom line: the person is not the Alpha Person for an emergency (hopefully you have other team members for this) but the person seems to be a dedicated expert, willing to support colleagues in the team based on the skillset.

Of course NO . Why he has to work after 5 , if he come on time like you mention ????

If you already now that he leave at 5 , why you don´t planning ahead ??

Talk with that person and make some flexible schedule . Talk, talk talk, talk , there seems to be a gap in communication between you..

BR

This team member needs to be open an tell you why he will not be available after 5pm.

If it is for family reasons then that explains a lot. Ask if it is only temporary or a permanent schedule.