First try forcing a video output reset: turn the PS5 completely off, wait about 30 seconds, and when you turn it back on hold the eject button until you hear two beeps (takes about 7-10 seconds). This forces the console to reset its resolution and sometimes fixes this random no-signal issue. While the PS5 is booting in that safe mode, make sure your TV is already on and set to the correct HDMI input so you can see if anything shows up.
If that doesn't work, unplug the PS5 from the power outlet for about 2-3 full minutes, then plug it back in. Sometimes that HDMI output capacitor gets a bit glitchy and needs to discharge. While you're doing that, take the chance to check if the HDMI cable is really firmly plugged in on both ends - it's not just about touching it, it has to go in with real pressure. Also try a cable you know works well on another device, don't just swap it for some random new one.
Another thing that works is connecting the PS5 to a different TV (a friend's, a relative's, anywhere) to see if it's a console problem or specific to that TV. If you get signal on another TV, then the problem's in your TV's HDMI port or input settings. If you don't get signal anywhere else, then it's the PS5 that's got a stubborn video chip and that gets more complicated, but it's still worth trying that safe mode reset before calling a technician.