Well, shoot, we call this scenario "hurricane season".
If its a limited emergency, something like a Hurricane (been through plenty by now, weeks without power) the main things we ever ran off the genny was a fridge some lights and some plug in personal fans. Some things were used on sparsley, like a TV and DVD players for a movie, or when I was really desperate, my computer. For the most part, the lights, fan and fridge were the constants and they dont take that much of a draw. LED lights would make it even better.
However, 10 gallons of gas isnt a lot. Rationed properly to just lights and low power fans would stretch it out signifcantly, but then you wouldnt need the 5000w genny for that, and it wouldnt use the fuel as efficiently as a smaller genny for just those purposes.
I'd try to get more gas, if possible. 10 gallons wouldnt last us through most of the hurricanes we've been through (longest was over a month (i almost wanna say 2) without power, (back in 05). Anyways, we were one of the very last areas to get power back in two big hurricanes.
Moral of the story is, we did just fine. Didnt miss a beat. We were prepared, even in '04 before we had the genny and went through a couple 'canes. The big saving grace was that other areas HAD power and we could always drive somewhere for a bite to eat or in once case we got a hotel in Ft Lauderdale for a week and sat on the beach drinking margaritas.
If EVERYONE was out of power EVERYWHERE for more than a week..... 10 gallons wouldnt be enough.