Can I carry $5 K in cash with me, internationally, without getting into any trouble with the customs at the airport? ?

Depends on where you are going

However most countries limit it to $10,000 US or equivalent so check with that country's embassy before departure 

☆☆GYPSYFISH. Some countries charge hefty fees to use local ATMs with a US account. Plus they give very bad exchange rates unless you can find one that uses US currency 

☆☆☆☆☆☆MS. If leaving the US with $10,000 or more you must report to customs before departure. 

The laws vary with each country. On the forms you fill out when you arrive in a new country, you have to declare whether you have more than a certain amount of cash- it's usually $10,000, but it may be different in different areas.

I can't imagine a reason for carrying that much cash, unless you're a drug dealer. You can take money out of the ATM when you get there. 

Yes, just don't exceed $10,000.

Ummm... what is your departure and destination airports?

Depends on the customs laws of wherever you're travelling to

You don't go through customs when you leave a country.  No one has any idea how much money you are taking with you.  But countries DO have regulations about how much you can bring in before you must declare it.  That amount can vary by country (it is usually more than $5,000 though), so you need to look it up to be sure.

That depends on the laws in the country you're leaving from---a few countries only let you take out a certain amount of money, most don't care what you leave with--and the country you are entering. Most countries allow you to bring in up to 10,000 of whatever their currency is (dollars or euros, for example) before you must declare the currency when you enter that country. Not declaring is a big mistake. So check the laws for the two countries involved. There is no general rule for all countries.

you need to call the airlines and ask them