I'm applying for a personal loan of $5,000, but I have no account to deposit it into nor any money to open one at the time. What should I do?

Remember, not all banks require a substantial initial deposit.  Some can be as low as $50 or $100.  OR you can try several non-brick and mortar type banks (i.e. online) and many of them will give you incentives for joining.  I would check out banks like Capital One 360 Checkings or Savings (bonuses for signing up), Schwab Bank (hard pull, links to a brokerage account but can be used internationally for no fees), or a million other options you can find on a quick search.  Alternately you could open an account like Alliant Credit Union online, and they give you a $50 dividend to your checking, and $5 to your savings account upon opening and when you eventually fund the account.  It has a 1% annual interest yield which make it even more attractive then the low rate environment of traditional banks.  I know other banks like citibank are pretty easy to open online as well- they will also give you some time to fund the account.  By doing a little bit of research into online banking, this could certainly be a viable option.  Hope that helps!