I was reading of political violence that occurred in Turkey in the late 1970s between communists and ultranationalists, which led to around 5000 deaths before the 1980 coup. Was such violence felt outside of the major cities, and were there credible threats of a major uprising by either of the factions?
Yes. Yes, that is, if it was not already a quasi-civil war anyway.
The epicentre of the violence was indeed the major cities as you have said. But by no means the violence was limited to these cities. To begin with, the left-wing armed groups adopted a roughly Maoist vision of revolution according to which the revolution would come from the rural areas. A large number of left-wing groups were active in rural areas as a result: THKO, THKP-C, TİİKP... The examples can be easily enumerated. Similarly, the nationalists too had a structure of organisation that allowed them to be present in many rural areas.
Consider the massacre in Çorum in May-July 1980. The fighting involved both left-right wing militants and a pogrom against Alevites in town. Around the same time, Fatsa, another rural town, was declared 'freed zone' by the left-wing militants and the leftist mayor. That meant self-rule for the town, that is. The army moved in and removed leftist groups by force, following deadly clashes. In the 1970s such things were not are at all, unfortunately. The massacre in Maraş, in December 1978 is yet another example.
Both left-wing and right-wing groups had the power and intransigency to turn the situation into a civil war in the late 1970s. The situation was worsened by the fact that the government(s) were weak, the security forces themselves were divided (the police forces belonged to two unions, one nationalist and one leftist), and so on. So the situation was already something very much reminiscent of a civil war. That it did not become a full-blown civil war is probably due only to the fact that people, in general, found armed groups too marginal and radical. So when you look at the ballots, the leading left-wing party is by far the Republican People's Party of Bülent Ecevit; a leftist surely but who openly condemns violence from 'fascists' and far-left alike. On the right, the most significant figure is Süleyman Demirel of the Justice Party, who is more like a typical American centre-rightist then a fascist, however you define the word. Ex-colonel Alparslan Türkeş's Nationalist Movement Party was very strong and had a military-like disciplined organisation in towns and cities, but when it came to elections, they were barely a significant party. The same holds for the more radical leftist parties. Even the Labour Party of Turkey which was much more hesitant in terms of use of force was an outsider in terms of parliamentary politics. Islamists always got more votes, but they were also far less active on the streets than the nationalists or the leftists.
That said, maybe if the Army did not intervene and overthrow the democratic government, polarisation would go on and at some stage lead the centre to collapse to the benefit of far-right and far-left. That sort of a thing is not impossible; especially when the centre proves its weakness time and again. This is not, of course, to say that the coup d'etat was legitimate. This just means that, perhaps, with time polarisation would become more pronounced and violent and would lead to a full-blown civil war. The leftists could not initiate a rebellion and actively control a part of the country for a long time under any circumstances, but a civil war is possible even without this, so the answer is still yes.