Does routinely shifting a manual trans from 1st to 3rd to 5th create any issues.?

You can skip a gear if the driving condition demands it. It’s all about adjusting to the revs when you skip a gear.

When skipping a gear with a manual, the revs will take slightly longer to drop from high revs to lower revs. If you shift from third to fifth gear and let the clutch out at the same speed as normal, the car will jerk as it works to settle the unbalance. Instead, waiting just a little longer to let the clutch out will keep things matched equally as the gearbox moves to meet a lower rev level.

When down shifting, it's a little more tricky. Rev matching is essential when shifting from a low to high gear. For example, if you're driving along the highway and you want to pass a slower moving vehicle, a shift from fifth to third may be in order. Rev matching the engine to the clutch will keep the car from jerking, and in the worst case, locking up the wheels. When the clutch speed and engine speed meet, they should be in near-perfect harmony. Plus, no one looks good under revving a car while down shifting. Clutch wear will also creep up on you, too.

You can also start moving from a standstill in a gear other than first, but it's going to cause slightly more clutch wear.