The 1st CS.IAP was formed at Ivanovo and Kubinka air bases, and, after taking some formation with the La-5UTI (the two-seater trainer variant of the La-5) by June 1944 it was declared as combat ready.
During the Slovak National Uprising, Jan Golian (leader of the Slovak rebels) asked the USSR for help, so the VVS sent the 1st CS.IAP which was stationed at Proskurov airfield, near Lviv, in the Ukrainian SSR. On 17th September 1944 they were rebased to Zolna airfield and, by 18th September they were already in action as they attacked the Luftwaffe base in Piest'any (Bratislava) destroying various enemy fighters. Shortly later, on the 20th they also attacked the Malacky-Novy-Dvor air base destroying more Luftwaffe aircraft to prevent them from intercepting American bombers of the 15th Air Force. Those attacks took the Germans by surprise, so they had to move both Schlachtgeschwader 77 and Jagdgeschwader 52 from southern Poland and Hungary respectively to fight against 1st CS.IAP. During the Slovak National Uprising they provided aerial support by attacking German artillery positions and strafing ground troops, having to overcome the unsuitability of the La-5FN for the ground support as it lacked armour.
When the uprising failed and the Germans retook the Slovak land, the 1st CS.IAP escaped back to Soviet lines. It was during this period that the unit flew a total of 573 sorties and destroyed 13 enemy aircraft with ten casualties.
The unit was transferred to the newly created 1st Czechoslovak Independent Combined Air Division on 25th January 1945 and it served during the Soviet advances in southern Poland and Czechoslovakia providing aerial support to the 4th Ukrainian Front.
After spending some time at Przemysl airfield the 1st CS.IAP was transferred to Poremba airfield from where they took off in their last mission escorting a formation of eight Il-2 Shturmovik attack planes bombing the village of Olza, in southern Poland.
There was a second Czechoslovak Fighter Regiment undergoing training, but the war in Europe ended before their training could be completed.
The La-5FN was designated as 'S-95' in CAF service and the type had to be constantly overhauled as they were phased out in the USSR back in 1945. In July 1946 a group of Soviet specialists declared all but two La-5 non-airworthy and directed the fighters to be scrapped, discarding the order for an additional force of 60 La-7 (the successor of the La-5) to be delivered.
After a further inspection by the CAF and the Czechoslovak Scientific Aviation Institute, the La-5 were declared mostly flyable, except for aerobatics purposes. However, on static tests carried out on both La-5FN and La-5UTIs, the wooden parts showed signs of exhaustion and so, every La plane was grounded on 13th December 1946.
Anyway, after further inspection, it turned out that the wooden airframe and other parts, were already counted in their calculations, so, during 1947 the La-5 was admitted again into the CAF. By 1st July 1948 the CAF had 23 La-5FN and LA-5UTI in strength but, by late 1948 the type was already being withdrawn from service.
The last official unit to employ the La-5FN and La-5UTI was the Bezpecnostní letectvo, the aerial branch of the SNB (Czechoslovak National Police which existed from 1945 to 1991).
2nd https://en.wikipedia.org/wiki/1st_Czechoslovak_Fighter_Air_Regiment