I attempted to pay the rent the last day of grace period, however, the office was closed and I had to pay late fee. Can I sue?

You can but it will likely cost you more than $90 in filing fees and court costs and taking off work for a day to sit in court. From a shear cost/benefit analysis, probably financially worthwhile.

You want to sue THEM because YOU paid late? Even if you have a grace period, the property managment company can begin eviction proceedings the day after you missed your payment (i.e.. during the grace period). You're lucky they are not evicting you. No you can't sue them.

The 5 day period is not a grace period. Your rent is due on the first, period. The landlord can file an action for failure to pay rent on the second because your rent is late, They may not, however, charge you a late fee until after e 5th - that's what the 5 days if for. What exactly is it that you think the landlord has done that's actionable?