For the first week I was OK with pressing F12 to enter the firmware (“BIOS”) setup each time I wanted to boot into elementary, but I finally bit the bullet and did a proper re-installation since I got tired of not having a working boot manager (i.e, GRUB2). This time, I did my homework and read up on EFI, disabled support for legacy mode in the firmware in order to install elementary in EFI mode, and started the installation from the USB. In the installer I selected the existing ~500MB EFI partition (that also holds the Windows EFI binaries) for installation of GRUB2, mounting it at /boot/efi. I rebooted and – voilà, there was the much sought-after GRUB2 menu, although barely readable since it chose the native 3840 x 2160 resolution (This was fixed later by setting GRUB_GFXMODE=1280×1024 in /etc/default/grub and running update-grub)
So, now I can at least say that I have a basic understanding of how EFI works. And the 5510 now dual-boots just as fine as my old Latitude.