boost 100ns pulse from 5 v to 10 v
You could consider just using a fast comparator such as a LM1711/1712 

They will operate with a 10V or even 12V supply. At currents of 1mA or less you'll get almost the whole supply swing at the output. 

Output rise and fall times are in the 2ns range with a 10pF load, and propagation delay is less than 5ns typically with 20mV overdrive. 



A more Neanderthal method would be to drive the gate of a smallish MOSFET such as an 2N7002 hard with something like a fast CMOS inverting buffer and use a very low value of pullup resistor to 10V or 12V (something like 100 ohms, which would consume 100-120mA with your very low duty cycle. 

Minimize loop inductance by keeping everything very compact and use very good supply bypassing right near the transistor/resistor.