OK.... You have a couple of options here.
First... from a powered down state.... hold the up volume and power button for about 10-20 seconds. Then hold the down volume and power button. It SHOULD turn on and go into the backup bootloader screen. The 5 has a secondary, backup bootloader (I learned about this when the Hellscore app borked my primary bootloader when it laid down the Nexus 4 kernel on top of it.. serves me right for trying to save some time).
If it stays in the bootloader now, at least you can go from there. If it STILL doesn't stay powered on, your toast. Something, probably in the power circuitry, is junk. The Nexus 5 is near impossible to brick because of a software problem. You can recovery from just about EVERYTHING.... well, short of something overwriting the primary AND backup bootloaders. But pretty much anything else can be recovered as long as it isn't something with the hardware.
If it stays up, from there, go in and clear your cache and reboot. That's might be a shot in the dark.... I'm guessing that your issue isn't just a corrupt cache. Reboot and see if you can get it to stay up. If not... repeat the above to get into the bootloader... do a factory reset.
Yeah, factory resets suck, but hopefully you loaded a custom recovery when you rooted and have a relatively recent system backup you can fall back on. If you DON'T and got your phone up and running.... LOAD A CUSTOM RECOVERY AND MAKE A BACKUP.