BJT driver, high peaks in power
The power rating on transistors is typically for the continuous power. What you have here is 5W for 1μs, once every two milliseconds. This comes to 1μJ of energy going into your transistor every two milliseconds, which is an average power of half a milliwatt on top of whatever else is going on. So, based on energy alone you're probably fine--I'd be surprised if a 2N3904 burned out due to such low-energy peaks.

However, I can't seem to find any data on maximum pulsed current ratings. The 2N3904 is rated for 300mA continuous collector current, but it seems pulsed current isn't a standard figure of merit. I suspect that your transistors will be fine, unless that current pulse goes up to something ridiculous like 50A.

That's all assuming an unmodified circuit, though, and an accurate simulation. It's entirely possible, likely in fact, that parasitic elements that aren't simulated would stop this from even happening in the first place. And as @jonk says in the comments, if it is a problem, you can always slap a few ferrite beads on to spread the energy out over time, reducing the peaks.