Opinions on Shimano 105 10-speed STI transmission ??

As @hill_climb says, a tight angle around the bars under the tape can be a real problem. Some bars have way less than the recommended minimum 80-100mm internal radius. Sometimes they are installed without Shimano's recommended plastic cable tunnel. It's also better to run the gear cable on the front, next to the brake cable, than around the back of the bar. A tight cable radius made my 6700 setup (virtually identical to 5700) initially absolutely horrible. The rear mech would take 5 turns of the crank to get to the correct cog. Really annoying!

Also make sure when you put the new cables on, to flare out the hole at the end using the tool on the side of the Park cable cutters, or a spare bit of wire. A tight cut on the end of the inner can produce a dreadful grating cable motion. And if you've moved the bars, you'll find that you need to recut the cables to get the best large radius on the cables leading to the down tube. Best if the two gear cables cross under the stem and enter on the far side of the downtube, thus crossing inside the downtube to exit on the correct side of the bottom bracket guide. If you see what I mean!

When my (Tigra) 10 speed transmission was new, I found it needed frequent adjustment over the first 1000 miles or so, as the cable took a while to bed itself in - and then after that it was suddenly fine and reliable.

As many have said, a 10 speed 105/tiagra mix has been faultless for me in the past. I did 3000 miles on that set up last year in all weather conditions and it behaved pretty much faultlessly. I didn't lube the cables once in that time - all it needed was chain lube and occasional gear tweaks as the cables stretched. Tight radius bends in the cable routing definitely sound like they could be the problem.

clean any grease from the bb guide .... a little spray teflon is about all that needs
as anymore attracts dust/dirt/debris from the front wheel making changes
crunchy at best .....

be careful when you shorten the outers, to short is as bad as too long, you need good smooth curves, this includes at the rear mech, depending a the frame routing sometimes the outer at the rear mech looks way to long, but you really need that smooth arc

ditto everyone about lubrication, it will cause more problems in the long run, use decent outers like Jag or Shimano's own.

If you are going to get new cables done at a bike shop, make sure they know what they are doing, just because they have the tools, don't mean they know what they are doing as anyone that been into the the big Orange shop will attest to, and for the price some places charge, you can buy the right tools, watch a few decent videos like the ones from Art Cycles or Park tool and you are set for life

I had a similar problem it turned out my outer between the frame and rear mech was too small to it was causing allot of resistance try running a new cable with what my mechanic called a f**k off outer

As per joemmo, never had any issues with 105 10speed or Ultegra 10 speed (essentially the same shifter but a carbon lever).

I wouldn't put grease anywhere near the cables on my bike (brake or gear), but I would use a light dry lube to minimise the friction and work as a corrosion inhibitor. If its both front and rear gears then it could be the grease around the bb where both cables pass.

Cable outers can also shift slightly under bar tape through riding or in the event your bars get too twisted e.g. lifting in/out of a car boot etc.

I'd get new cables (inners and outers) professionally fitted with new bar tape and if its done properly that should sort any issues.

It sounds an unusual issue to degrade so quickly but one thing I would do is to stop greasing the cable guide under the bottom bracket. It will only attract grit and dirt as you ride, they generally work better 'dry' or with a very light lube. If the cable sticks here then this might explain why the front mech is reluctant to shift onto the smaller ring.

It sounds most likely to be a cabling problem though. You don't say if you are lubricating cables but again, they tend to work better with whatever lube or teflon type coating they came with, If you flush this out with spray oil it doesn't always make things better.

If you have the 5700 series 105 levers with the cables under the tape then they can suffer from having the cable bend tight around the inside of the bar. If it persists then you could replace the stock shimano cables (which on the whole are not bad) with some aftermarket ones like Jagwire for example.

One final thought, inner cables do not stretch as such, what tends to happen is the outer and ferrules can compress and generally settle into the cable stops resulting in slack. If you are slackening off cables to oil them then each time you take up the slack then you are inviting movement and then re-settling.

Hmm, never heard of a problem with 105 shifters. Are you tightening cables off enough on your derailieurs? Are your outer cables properly seated in the frame and in the shifters?