Prayer is the second pillar of Islam, and is mentioned probably over 100 times in the Qur'an. Failing to perform prayer during the prescribed times is a sin: It's listed as Major Sin 4 in Major Sins by Imam Shamsu ed-Deen Dhahabi (pdf). See also If someone do not pray 5 time, is he/she Kafer?
...why do none of the Muslims that I know do that?
They will have their own individual reasons; it's not appropriate to speculate. However, maybe they actually perform their five prayers, but you just don't notice. When I've asked people in the past, they've replied: "I pray in my heart", "I'm not all that devout", and "we only need to pray three times per day". I pray five times per day.
Is there some sort of automatic dispensation from the requirement to pray if you live in a non-Muslim country?
No. IslamWeb write:
With respect to the matter of immigration from a non-Muslim country to a Muslim country ... Those who cannot fulfill their religious obligations and commands, or fear temptation, (i.e., face hardship due to the bad environment and the prevalence of disbelief in the place where they dwell). These Muslims are obliged to migrate.
And if they are breaking the rules, what are the consequences? Will Allah punish them in Hell? Will they only get 71 virgins in heaven instead of 72? (I mean no disrespect in saying that)
Only Allah decides who goes to Hell or not. This is what He says (translated into English):
But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil - Except those who repent, believe and do righteousness; for those will enter Paradise and will not be wronged at all. -- Qur'an 19:59-60
O you who have believed, let not your wealth and your children divert you from remembrance of Allah. And whoever does that - then those are the losers. -- Qur'an 63:9
So woe to those who pray [But] who are heedless of their prayer -- Qur'an 107:4-5
(It's possible the 72 virgins thing is just made up: Do Muslim martyrs really get 72 virgins in heaven?)
It will be questioned on the Day of Resurrection:
It was narrated from Abu Hurairah that the Prophet (ﷺ) said:
"The first thing for which a person will be brought to account on the Day of Resurrection will be his Salah. If it is found to be complete then it will be recorded as complete, and if anything is lacking He will say: 'Look and see if you can find any voluntary prayers with which to complete what he neglected of his obligatory prayers.' Then the rest of his deeds will be reckoned in like manner." -- Sunan an-Nasa'i 466 [grade: sahih] (sunnah.com)
In short, what happens if you fail to pray five times a day?
Aside from it being obligatory, there's a range of benefits to prayer; see e.g. bakkah.net. There's a section "The Benefits of Performing Prayers" listed in Major Sins above. One important one is
Narrated Abu Huraira: I heard Allah's Messenger (ﷺ) saying, "If there was a river at the door of anyone of you and he took a bath in it five times a day would you notice any dirt on him?" They said, "Not a trace of dirt would be left." The Prophet (ﷺ) added, "That is the example of the five prayers with which Allah blots out (annuls) evil deeds." -- Sahih al-Bukhari 528 (sunnah.com)