When playing the short club convention I thought a one diamond bid shows that I hold five diamonds. Is that true?
As Alexander Woo says in a comment, there is no "short club convention" - at least, no single one. Frankly, there is no "X convention" for any X - you will find people who play X a different way than you, and will insist theirs is the right way (or even the only way). The correct answer to your question is "what have you and your partner agreed to?" and "how are your responses tuned to fit that agreement?" It is always a risk to say "we play X" and assume partner plays it the same as you do.
"Short Club" systems common enough for me to think of immediately include:
The most common "short club" played by thousands of (usually weaker) players at home and in tournaments: "5-card majors, 4-card diamonds, 3 cards clubs, with 4=4=3=2 opened 1 club instead of 1 diamond" (= is a writing convention meaning "suits in order", so 4=4=3=2 is 4 in both majors, 3 diamonds, 2 clubs). Perfectly playable, as long as it doesn't evolve into "I couldn't raise on 5, what if you only had two!" or other monstrous convolutions to care for this very rare (3% in a strong NT) hand type. In this case, no, 1 diamond does not promise 5 (1D is opened on 3=3=4=3, for example).
A very common system in my area is "Montréal Relay", where 1 diamond does promise 5, 1 club is frequently 2 (the key of this system is that the "relay", 1C-1D is catchall, and only "denies a 5-card major" (and a few other rare hands)). Now the issue is what to do with 4=4=4=1; some put it into 1C, some into 1D, some play some sort of 2D 4441 bid,... I am amused by the fact that there are more players of Montréal Relay where I live out West, than there are in Montréal itself.
Becoming more common in the ACBL (due to convention liberalization), and very common elsewhere, is 1 club "clubs or balanced", usually with transfer responses (so 1C-1D shows 4+ hearts, 1C-1H shows 4+ spades,...) Here, 1D is almost always unbalanced, almost always 5 (could be 4=4=4=1, many play not 3=3=5=2 or (32)=5=3).
Then there are all the two-way and three-way club systems like Swedish ("weak NT or strong hand") and Polish ("weak NT or 15-19 clubs or strong hand") Clubs. The rules for those vary a lot as well, but we're leaving the world of what would be called a "short club" convention.
Of course, there's the really old-fashioned "short club", where as well as the clubs hands, you open 1 club with a hand not quite strong enough to open a strong 2. 1C is "not forcing", but partner knows not to pass it, "just in case".
This system works much better with the similarly old-fashioned spoken bidding clues, where, as Ron Andersen (prolific bridge author, teacher and expert player) said about his "mother's bridge club" (quoting from memory):
If a player has 13 or so with real clubs, she opens "one club". If it's 3 poor (or 2) clubs, she opens "a club". If she has a strong hand that shouldn't be passed, it's "I'll start with a club".
In case it wasn't obvious, this "help" is highly unethical if done by habit, and cheating if on purpose. Don't.
The "Standard American" style is to open 1 diamond with 4-4-3-2 distribution (and not enough points to open 1 No Trump.) Some pairs agree to open this hand 1 club instead, so that 1 diamond always promises at least 4 diamonds. Regardless of one's preferences here, though, 1 diamond is still the natural opener with 4-4-4-1 distribution.