The rent is due on the first & no later than the 5th of the month or there will be a late charge. They are often late but ignore the late charge. Is that anything I can do about this/

Yes... total up the late charges they owe you... give them a 3 day pay or quit notice. And hold them in breach of lease the next time they are late. Which is grounds for eviction.

The bigger question is how good are they otherwise and how hard was it to rent the place out?
I would send a total of the late charges too, just to make it clear that the terms of payment aren't hot air, and add a note saying something to the effect that good tenants don't get rent increases, late ones do, to cover the late fees on your mortgage - and some get terminated at the end of the term or even evicted.
(Doesn't matter if you incur mortgage fees or not. If you want to be a bit more truthful, just say late fees on your bills.)

I would send them a statement of their current arrears. I would tell them that since they have not paid all they owe that EVERY rent payment is therefore late and will incur a further late charge until they bring their account up to date. The statement should also make it clear that you will use all legal means available to collect what is owed.

Note, you WILL be able to deduct any outstanding fields from their security deposit.

But, as Joy notes, how good is the tenant otherwise? If their being late is not costing you money, then it might be better to just take it out of the security deposit when they vacate.

... The rent is due on the first & no later than the 5th of the month or there will be a late charge. ...

In other words, the rent is due on the 5th. The part about the 1st is simply empty words, it appears to me.

Late after the 1st or 5th? Way I read it is they can pay up to the 5th without penalty.

In many states, the 5th is the law... haven't looked up NY. Seems to me when I was a LL in MA it was the 10th!

Hence my suggestion of 'fast paying tenants get rewarded, late ones get rent hikes.' And yes, that's legal.
(There are a very few communities that limit how much you can raise rent, percentage wise, from one year to the next. I think NYC is one.)

Washington DC is another place that seriously limits the ammounts of increases. Why anyone would want to be a landlord in DC is boeyond me, they are so anti-landlord I'd want nothing to do with the place.