ACH is actually safer. When you establish an ACH link, the bank and account is verified, either traditionally with test deposits or through instant verification. Then you can simply transfer the money between the banks by selecting from a dropdown menu. Not sure why your ACH will take 5+ days, usually 1-2 days, but they may hold the funds for a few more business days if your account is new.

Wire fund is immediately available same day, but usually the sending bank would charge a fee for that. There is also the low possibility of an error in wiring that can make your money disappear for as long as it takes for the receiving bank to track down. However, usually if there is an error in wiring or the receiving bank rejects it, you get the money back to your sending bank immediately.

I prefer ACH, as I don't like to pay fees and I have anxiety when I type routing and accounting numbers.