Pay off the credit card. You'll incur ~3% charge to make the transfer, right? Assuming things land around -7% today, you're talking about a 4% net gain back to yesterday's close. Things could get a lot worse on an uncertain time frame before they get better. Not worth the risk.
I couldn't care less about how long it takes markets to recover (since I have faith that they will, eventually); once I buy the money would stay in for at least a decade, and realistically much longer.
Also, more details about the situation: the CC rate doesn't expire until 8/23, and (given my wife's relatively-lucrative temporary job) we're currently cash-flow-positive by several thousand dollars a month,
after subtracting out our normal periodic investing (maxing 401k and IRAs at $2416.67/month). In other words, it's entirely reasonable that I could drop the money I currently have saved into the market today, then save it up
again starting from $0 in the two months before the payment is due. It'd be a little tight, but doable (in fact, that might be a good thing -- I've been getting a little lax in my spending recently, and that might help fix it!). If I didn't invest this $5K today, I'd almost certainly be investing that next $5K in a couple months anyway. Rolling over the entire $5K CC balance would represent either a worst-case scenario or a calculated decision based on an even more extreme drop in the markets.
So, thinking it through some more, it seems like the risk I'm taking is that (a) something would happen to force me to roll over the balance or (b) the markets would continue to drop over the next few months, making waiting to invest better, vs. the assumptions that (c) today is a "Really Bad Day" allowing an abnormal >4% "panic discount" and (d) on average, markets go up (meaning that by default I plan as if the price will be higher in a few months).