IPO valuation is super sophisticated. There is usually a Managing Underwriter, who has a team of analysts/asset pricers/investment bankers/lawyers/etc. with complicated terms and they go and value a company. They usually take control, assess and decide what share price is "suitable" for the company to go public. This team usually takes 7% commission and they love high-valuation companies with high risks.
Example of $LYFT
by Chris in the comment is just fantastic and here is LYFT ratings by analysts:
Apr-02-19 Initiated Seaport Global Securities Sell $42
Apr-02-19 Initiated Cross Research Buy
Apr-01-19 Initiated Guggenheim Neutral
Apr-01-19 Initiated Consumer Edge Research Neutral $73
Reference: LYFT Rating by Analysts

Reference: IPO Prospectus for LYFT
LYFT has $43
net loss per share. Basically, these types of companies go public to reduce the risks and they will keep going down to a 52-weeks low, due to so much debts that they hold. There is usually a 6 months lock-up period that they cannot sell their shares. For such company, you cannot set a $5
per share price because the company can become prone to bankruptcy. They usually double or triple that net loss price and send it "public".
$10-$20
is a good price range for high caps. However, a high-cap company has to be super healthy to go through such price range, such as Facebook which IPOed at $19
and doubled to $38 in the first quarter.
Another factor you might consider is the size of company, amount of money they want to raise and ratio of desired capital to market cap:
High Market Cap
Mid Market Cap
Small Market Cap
There are also many investing/trading factors to consider such as sector
, industry
, market competition
, stock competition
, exchange market
, share float
, debt to equity ratio
, earnings per share
, earnings per employee
, assets/liabilities ratio
and so many other factors/ratios that are important.
IPO share price also depends on the company's business strategy, if they want to be super public or just public. Companies that like to be super public are always in Media such as FAANG.
This book might be helpful for you to take a look.
\$5 Share Price
$5
is a high risk price, because it can easily drop to $1-$2
and many investors are just not fond of such prices.
\$10 Share Price
$10
is fine, which can drop to higher single digit ($5-$9
).
In sum, IPO share pricing depends on so many financial, technical and strategical factors.