Hi Maureen,
Yes of course, as already pointed out, you have everyright to know what each bid means. Your opponents were using superprecison with the "greek asking bids". These have fallen somewhat out of favor among precision players, I am not exactly sure why, as they are still useful. Here tney used the GAMMA trump support asking bid (2S), epsilon (3D, 4C, 5H) and repeat epsilon asking bid (5C).
I would have made only a change in their auction. I would have started with a Beta control asking bid (1NT), to which partner would have responded 2H (4 controls). Now 2S is still the gamma ask and the new suits are still epsilon, but you go in knowing partner has two aces or an ace and two kings (from the 2H response and your own hand).
If one adopts superprecision asking bids, you have to know when not to use them. I most often bid 1C-1S-2NT or 1C-1S-3S to revert to natural bidding when my hand was not suited for a series of tons of bids.
The advantage of 1C-1S-1NT sequence instead of immediately bidding 2S is that if partner has some yucky positive response like S-Jxxxx H-KJxx DQJx C-KQx you get to end the auction very quickly....
1C-1S
1N-2C (2C = 0 to 2 controls, not enough for slam)
4S
Ben

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