I wouldn't expect the terminal emulator or screen/tmux to cause a 5s delay in this situation; and if they did, I'd expect them to cause it in neovim as well as in vim.
This does happen with neovim too. In fact, I had this issue in neovim even though I hadn't had it in vim. It was a one-line config change in my tmux.conf to fix it though, so no skin off my nose.