Frustrated because I find objects worth over 5,000 gold sometimes, yet there's no merchant with that much gold. How do you handle this problem?

Depends on the item. Sometimes I can finally offload it to someone who's a merchant and trainer, both, by getting some training (which boosts their gold), then selling them the expensive item and getting my gold back. This works especially well on my current mage character when she gets useless--but expensive--robes: at least the CoW trainers buy robes and jewelry. Doesn't always work out that well, though, if they don't buy the type of item I need to sell.

You could always try a similar strategy: beefing up the merchant's gold reserve by buying a bunch of smaller, less expensive items, then selling the expensive item to them and recouping your gold.

This.

Especially as an Alchemist, your items/potions can be worth several times more than what the merchant has.

I get to a point where I browse for anything and everything in their inventory that will be useful in some way, clean them out, leave the junk, and then sell my wares.

It depends what sort of character you have, but:

Archers - The most expensive arrows (0 weight)

Smiths - Ores/Ingots/Jewels

Enchanters - Any enchanted gear you haven't already learned the enchantment for

House builders - All that misc stuff - straw/glass/goat horns etc

etc etc etc.

And yes - trainers are also handy. Most mages as mentioned above, and also Grelka in Riften, for light armour (which I find one of the more difficult skills to level as light armour is designed so that you can actually avoid being hit)

-HK