What kinds of changes would happen in our lives if the Earth's orbit around the Sun were increased by 5%?

This is an interesting question, as there are a few possible answers. I'll give a few possible situations below.

If the speed of the orbit of the Earth was sped up by 5% (to ~347 days in a year) but the actual rotation was not changed (still 24 hours in a day), we might not see too many changes. Growing seasons would be shortened and compacted together slightly, and animal migrations/hibernations would be effected, but if the change was gradual, these organisms might be able to adapt without too much trouble. If the change was sudden, it is not known what would happen as it would depend on the severity of the oncomming winter season. Certain reproductive cycles that are very sensitive to environmental changes may not be able to function so you could see extinction of certain species. If an early, strong winter was to come, already hastened by the increased orbit speed, massive food shortages caused by crop and animal die off could also be seen.

If the orbit was increased because of the earth moving closer to the sun, the changes would be due to an overall increase in temperatures around the globe.

If the orbit speed increase was caused by say, a large rocket straped to the earth pushing us 5% faster (yea, very unlikely... ) our orbit would very likely move out farther from the sun to restore a similar balanced period as we have now. Colder temps and a possibility of collision with other planets if we move far enough out.

In any case, with a faster orbit, we start moving into the path of space objects (comets, astroids, etc.) that would have avoided us had we stayed in our normal 365 day path around the sun.